1. A moving van leaves a house travelling at an average rate of 35 mi/hr. The family leaves the house 3/4 hour later following the same route in a car. They travel at an average rate of 50 mi/hr. How long it will take the car to catch up with the moving van?

Question

2. Juan drives to work. Because of traffic conditions, he averages 22 miles per hour. He returns home averaging 32 miles per hour. The total travel time is 2 1/4 hours. Find the time Juan spends driving to work.

Answer 1

in 3/4 hour, the van moves 26.25 mi
Since the family is going 15 mi/hr faster, it will take 26.25/15 = 1.75 hours to catch up

Answer 2

let the time taken by the family be t hours
then the time taken by the van = t+1/2 hours
for those times:
distance covered by family = 50t miles
distance covered by van = 35(t + 1/2) =35t + 25 miles
but at catch-up they must have gone the same distance, so
50t = 35t + 25
15t = 25
t = 25/15 hours = 5/3 hours or 1 hour and 40 minutes.

For the second, you have to base your equation on the fact that
the distance each way is the same

let that distance be d
time to go to work = distance/rate = d/22
time to return home = d/32

we are told that the total time is 2 1/4 or 9/4 hours

so ......
d/22 + d/32 = 9/4

hint: multiply each term by 352 , the LCD
and take over from there