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 for the problems. 1. House Construction This is an inverse proportion problem, meaning that as the number of men increases, the time taken to build the house decreases. The total amount of work (man-days) remains constant. Step 1: Calculate the total work in "man-days". Given that 15 men take 12 days to build a house: Total work = Number of men × Number of days Total work = 15 men × 12 days = 180 man-days Step 2: Calculate the time it would take for 8 men. To find out how long 8 men would take, divide the total work by the new number of men: Time = Total workNumber of men = 180 man-days8 men = 22.5 days It would take 22.5 days for 8 men to build the same type of house. 2. Shafa's Bike Ride First, we need to find the distance to Shafa's school using the initial speed and time. Then, we can calculate the time taken for different speeds. Step 1: Calculate the distance to school. Shafa's initial speed is 18 km/h and the time taken is 30 minutes. Convert 30 minutes to hours: 30 minutes = (30)/(60) hours = 0.5 hours Now, calculate the distance using the formula Distance = Speed × Time: Distance = 18 km/h × 0.5 hours = 9 km The distance to Shafa's school is 9 km. Now, calculate the time taken at different speeds: a) At a speed of 9 km/h: Time = DistanceSpeed = 9 km9 km/h = 1 hour This is equivalent to 1 × 60 = 60 minutes. It would take 1 hour (or 60 minutes) at 9 km/h. b) At a speed of 20 km/h: Time = DistanceSpeed = 9 km20 km/h = 0.45 hours To convert to minutes: 0.45 hours × 60 minutes/hour = 27 minutes. It would take 0.45 hours (or 27 minutes) at 20 km/h. c) At a speed of 14 km/h: Time = DistanceSpeed = 9 km14 km/h ≈ 0.6428 hours To convert to minutes: 0.6428 hours × 60 minutes/hour ≈ 38.57 minutes. It would take approximately 0.64 hours (or 38.57 minutes) at 14 km/h. 3 done, 2 left today. You're making progress.