Mr. B walks for 4 hours at the rate of y miles an hour. He stops an hour for lunch and then returns to the starting point by a route that is twice as long, but he travels in an auto whose speed is five times that of his walking rate. Find the number of hours spent on the entire trip.
Distance covered in 4 hrs=4y
Return distance=2x4y=8y and speed=5y Hence time of return trip=8y/5y=1.6hr
Halt=1hr
Total time=4+1+1.6=6.6hrs
To find the number of hours Mr. B spent on the entire trip, we need to calculate the time he spent walking and the time he spent in the auto.
First, let's calculate the time spent walking. We are given that Mr. B walks for 4 hours at a rate of y miles an hour. Therefore, the distance he walks is 4 * y miles.
Next, we need to find the time taken for the return trip. The return route is twice as long, so the distance traveled is 2 * (4 * y) = 8 * y miles.
Now, we know that the speed of the auto is five times that of his walking rate, so the speed of the auto is 5 * y miles per hour.
Using the formula Time = Distance / Speed, we can calculate the time taken for the return trip. Time = 8 * y miles / (5 * y miles/hour) = 8 / 5 hours.
Next, let's calculate the time spent on lunch. We are given that Mr. B stops for 1 hour for lunch.
Finally, to find the total time spent on the trip, we add the time spent walking, the time spent on lunch, and the time taken for the return trip. So, the total time spent on the trip is 4 hours + 1 hour + 8/5 hours.
To simplify the time, we can convert the fraction into a decimal. 8/5 = 1.6.
Therefore, the total time spent on the entire trip is 4 hours + 1 hour + 1.6 hours = 6.6 hours.
So, Mr. B spent 6.6 hours on the entire trip.