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.
ScanSolve AI Answer
Here are the solutions to the problems: Problem 31: Cyclists A and B Step 1: Calculate the time taken by Cyclist A. The formula for time is distance divided by speed (T = (D)/(S)). For Cyclist A: T_A = 20 km30 km/h = (2)/(3) hours Step 2: Calculate the time taken by Cyclist B. For Cyclist B: T_B = 20 km40 km/h = (1)/(2) hours Step 3: Calculate the difference in time in hours. T = T_A - T_B = (2)/(3) hours - (1)/(2) hours To subtract, find a common denominator, which is 6. T = (2 × 2)/(3 × 2) - (1 × 3)/(2 × 3) = (4)/(6) - (3)/(6) = (1)/(6) hours Step 4: Convert the difference in time from hours to minutes. There are 60 minutes in 1 hour. T_minutes = (1)/(6) hours × 60 minutes/hour T_minutes = (60)/(6) minutes = 10 minutes Cyclist A took 10 minutes more than Cyclist B. Problem 32: Capacity of a tank Step 1: Identify the dimensions of the tank. The tank is a rectangular prism (cuboid) with: Length (L) = 90 cm Width (W) = 80 cm Height (H) = 50 cm Step 2: Calculate the volume of the tank in cubic centimeters. The formula for the volume of a rectangular prism is V = L × W × H. V = 90 cm × 80 cm × 50 cm V = 7200 cm^2 × 50 cm V = 360000 cm^3 Step 3: Convert the volume from cubic centimeters to litres. We know that 1 litre = 1000 cm^3. To convert cubic centimeters to litres, divide by 1000. V_litres = 360000 cm^31000 cm^3/litre V_litres = 360 litres The capacity of the tank is 360 litres. Last free one today — make it count tomorrow, or type /upgrade for unlimited.