Two buses start from the same station at 9:00 a.m. and travel in opposite directions. The first bus travels at 72 km/h and the second bus at 48 km/h. When will they be 240 km apart?

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Asked on April 9, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

Accepted Answer · 2026-04-09T09:33:06.078Z

Here are the solutions to the questions. Question 17: Two buses start from the same station at 9:00 a.m. and travel in opposite directions. The first bus travels at a speed of 72 km/h. The second bus travels at a speed of 48 km/h. We need to find the time when they are 240 km apart. Step 1: Calculate the relative speed of the two buses. Since they are traveling in opposite directions, their speeds add up. Relative speed = 72 km/h + 48 km/h = 120 km/h Step 2: Calculate the time it takes for them to be 240 km apart. Using the formula Distance = Speed × Time: 240 km = 120 km/h × Time Time = 240 km120 km/h = 2 hours Step 3: Add the calculated time to the starting time. Starting time = 9:00 a.m. Time elapsed = 2 hours Final time = 9:00 a.m. + 2 hours = 11:00 a.m. The final answer is C. 11:00 a.m.. Question 18: A solid cuboid has length l = 7 cm, width w = 5 cm, and height h = 4 cm. Calculate its total surface area. Step 1: Recall the formula for the total surface area of a cuboid. A = 2(lw + lh + wh) Step 2: Substitute the given values into the formula. A = 2((7 cm)(5 cm) + (7 cm)(4 cm) + (5 cm)(4 cm)) A = 2(35 cm^2 + 28 cm^2 + 20 cm^2) A = 2(83 cm^2) A = 166 cm^2 The final answer is B. 166 cm^2. Question 19: In the diagram, PQ SR. We need to find the value of x. Step 1: Identify the angles. The angle given as 245^ is a reflex angle. The interior angle at the vertex between P and S is 360^ - 245^ = 115^. Step 2: Draw an auxiliary line through the vertex of the 115^ angle, parallel to PQ and SR. Let the vertex be T. Let the auxiliary line be MN such that MN PQ SR. The angle P and the angle formed by PT and MN (let's call it PTN) are alternate interior angles. So, PTN = x^. The angle S and the angle formed by ST and MN (let's call it STM) are alternate interior angles. So, STM = 68^. Step 3: Use the sum of the angles at vertex T. The interior angle at T is the sum of PTN and STM. 115^ = PTN + STM 115^ = x^ + 68^ Step 4: Solve for x. x = 115 - 68 x = 47 The final answer is B. 46. (Note: My calculation gives 47, but 46 is the closest option. There might be a slight discrepancy in the problem's options or diagram's exact values if it's not 47.) Let's recheck the calculation. 115 - 68 = 47. If the options are fixed, then there might be a rounding or slight error in the problem's design. Assuming the calculation is correct, x=47. If I must choose from the options, 46 is the closest. However, I will provide the calculated answer. Let's re-evaluate the problem. The diagram shows P and S as angles on the same side of the transversal. If we extend QP and RS to meet, it forms a triangle. Alternatively, consider the "C-shape" or consecutive interior angles. If we draw a line from P parallel to ST and intersecting SR at U. This doesn't seem simpler. Let's stick to the auxiliary line method. The angle inside the "bend" is 360^ - 245^ = 115^. Draw a line through the vertex of the 115^ angle, parallel to PQ and SR. Let the angle formed by PQ and the upper part of the transversal be x. Let the angle formed by SR and the lower part of the transversal be 68^. These two angles are alternate interior angles with the segments of the 115^ angle. So, x + 68 = 115. x = 115 - 68 = 47. Given the options, and the common practice in multiple-choice questions, it's possible that the intended answer is 46 due to a slight error in the question or options. However, based on the geometric properties, the value is 47. I will provide 47 as the calculated answer. If forced to choose from the options, 46 is the closest. Let's assume the options are correct and there might be a slight visual misinterpretation or rounding. If x=46, then 46+68 = 114. This would mean the interior angle was 114^, and the reflex angle was 360-114 = 246^. The diagram shows 245^. This is a very small difference. I will proceed with x=47. The final answer is 47. Question 20: Find the equation of the line parallel to 2y = 3(x-2) and passes through the point (2, 3). Step 1: Find the slope of the given line 2y = 3(x-2). 2y = 3x - 6 y = (3)/(2)x - (6)/(2) y = (3)/(2)x - 3 The slope of this line is m = (3)/(2). Step 2: Since the required line is parallel to this line, it will have the same slope. So, the slope of the new line is m = (3)/(2). Step 3: Use the point-slope form of a linear equation y - y_1 = m(x - x_1) with the slope m = (3)/(2) and the point (x_1, y_1) = (2, 3). y - 3 = (3)/(2)(x - 2) Step 4: Simplify the equation to match the options. y - 3 = (3)/(2)x - (3)/(2)(2) y - 3 = (3)/(2)x - 3 Add 3 to both sides: y = (3)/(2)x Comparing this with the given options, y = (3)/(2)x matches option C. The final answer is C. y = (3)/(2)x. Question 21: The expression (5x+3)/(6x(x+1)) will be undefined when x equals: Step 1: An algebraic expression is undefined when its denominator is equal to zero. Set the denominator to zero: 6x(x+1) = 0 Step 2: Solve for x. For the product of factors to be zero, at least one of the factors must be zero. Case 1: 6x = 0 x = (0)/(6) x = 0 Case 2: x+1 = 0 x = -1 So, the expression is undefined when x = 0 or x = -1. This can be written as the set \0, -1\. Comparing this with the given options, \0, -1\ matches option B. The final answer is B. \0, -1\.

Accepted Answer · 2026-04-09T09:33:06.078Z

Here are the solutions to the questions. Question 17: Two buses start from the same station at 9:00 a.m. and travel in opposite directions. The first bus travels at a speed of 72 km/h. The second bus travels at a speed of 48 km/h. We need to find the time when they are 240 km apart. Step 1: Calculate the relative speed of the two buses. Since they are traveling in opposite directions, their speeds add up. Relative speed = 72 km/h + 48 km/h = 120 km/h Step 2: Calculate the time it takes for them to be 240 km apart. Using the formula Distance = Speed × Time: 240 km = 120 km/h × Time Time = 240 km120 km/h = 2 hours Step 3: Add the calculated time to the starting time. Starting time = 9:00 a.m. Time elapsed = 2 hours Final time = 9:00 a.m. + 2 hours = 11:00 a.m. The final answer is C. 11:00 a.m.. Question 18: A solid cuboid has length l = 7 cm, width w = 5 cm, and height h = 4 cm. Calculate its total surface area. Step 1: Recall the formula for the total surface area of a cuboid. A = 2(lw + lh + wh) Step 2: Substitute the given values into the formula. A = 2((7 cm)(5 cm) + (7 cm)(4 cm) + (5 cm)(4 cm)) A = 2(35 cm^2 + 28 cm^2 + 20 cm^2) A = 2(83 cm^2) A = 166 cm^2 The final answer is B. 166 cm^2. Question 19: In the diagram, PQ SR. We need to find the value of x. Step 1: Identify the angles. The angle given as 245^ is a reflex angle. The interior angle at the vertex between P and S is 360^ - 245^ = 115^. Step 2: Draw an auxiliary line through the vertex of the 115^ angle, parallel to PQ and SR. Let the vertex be T. Let the auxiliary line be MN such that MN PQ SR. The angle P and the angle formed by PT and MN (let's call it PTN) are alternate interior angles. So, PTN = x^. The angle S and the angle formed by ST and MN (let's call it STM) are alternate interior angles. So, STM = 68^. Step 3: Use the sum of the angles at vertex T. The interior angle at T is the sum of PTN and STM. 115^ = PTN + STM 115^ = x^ + 68^ Step 4: Solve for x. x = 115 - 68 x = 47 The final answer is B. 46. (Note: My calculation gives 47, but 46 is the closest option. There might be a slight discrepancy in the problem's options or diagram's exact values if it's not 47.) Let's recheck the calculation. 115 - 68 = 47. If the options are fixed, then there might be a rounding or slight error in the problem's design. Assuming the calculation is correct, x=47. If I must choose from the options, 46 is the closest. However, I will provide the calculated answer. Let's re-evaluate the problem. The diagram shows P and S as angles on the same side of the transversal. If we extend QP and RS to meet, it forms a triangle. Alternatively, consider the "C-shape" or consecutive interior angles. If we draw a line from P parallel to ST and intersecting SR at U. This doesn't seem simpler. Let's stick to the auxiliary line method. The angle inside the "bend" is 360^ - 245^ = 115^. Draw a line through the vertex of the 115^ angle, parallel to PQ and SR. Let the angle formed by PQ and the upper part of the transversal be x. Let the angle formed by SR and the lower part of the transversal be 68^. These two angles are alternate interior angles with the segments of the 115^ angle. So, x + 68 = 115. x = 115 - 68 = 47. Given the options, and the common practice in multiple-choice questions, it's possible that the intended answer is 46 due to a slight error in the question or options. However, based on the geometric properties, the value is 47. I will provide 47 as the calculated answer. If forced to choose from the options, 46 is the closest. Let's assume the options are correct and there might be a slight visual misinterpretation or rounding. If x=46, then 46+68 = 114. This would mean the interior angle was 114^, and the reflex angle was 360-114 = 246^. The diagram shows 245^. This is a very small difference. I will proceed with x=47. The final answer is 47. Question 20: Find the equation of the line parallel to 2y = 3(x-2) and passes through the point (2, 3). Step 1: Find the slope of the given line 2y = 3(x-2). 2y = 3x - 6 y = (3)/(2)x - (6)/(2) y = (3)/(2)x - 3 The slope of this line is m = (3)/(2). Step 2: Since the required line is parallel to this line, it will have the same slope. So, the slope of the new line is m = (3)/(2). Step 3: Use the point-slope form of a linear equation y - y_1 = m(x - x_1) with the slope m = (3)/(2) and the point (x_1, y_1) = (2, 3). y - 3 = (3)/(2)(x - 2) Step 4: Simplify the equation to match the options. y - 3 = (3)/(2)x - (3)/(2)(2) y - 3 = (3)/(2)x - 3 Add 3 to both sides: y = (3)/(2)x Comparing this with the given options, y = (3)/(2)x matches option C. The final answer is C. y = (3)/(2)x. Question 21: The expression (5x+3)/(6x(x+1)) will be undefined when x equals: Step 1: An algebraic expression is undefined when its denominator is equal to zero. Set the denominator to zero: 6x(x+1) = 0 Step 2: Solve for x. For the product of factors to be zero, at least one of the factors must be zero. Case 1: 6x = 0 x = (0)/(6) x = 0 Case 2: x+1 = 0 x = -1 So, the expression is undefined when x = 0 or x = -1. This can be written as the set \0, -1\. Comparing this with the given options, \0, -1\ matches option B. The final answer is B. \0, -1\.

Two buses start from the same station at 9:00 a.m. and travel in opposite directions. The first bus travels at 72 km/h and the second bus at 48 km/h. When will they be 240 km apart?

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Two buses start from the same station at 9:00 a.m. and travel in opposite directions. The first bus travels at 72 km/h and the second bus at 48 km/h. When will they be 240 km apart?

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