Question 102349
A moving van leaves a house traveling at an average rate of 35 mi/h.The family
leaves the house hour later following the same route in a car.They travel at
an average rate of 50 mi/h. How long after the moving van leaves the house will
the car catch up with the van?
:
Let t = travel time of the van when the car overtakes it
then
(t-1) = travel time of the car when this happens
:
They will have traveled the same distance when the car overtakes the van
Write a distance equation from the fact. Distance = speed * time
:
Car dist  =  van dist
50(t-1) = 35t
50t - 50 = 35t
50t - 35t = +50
15t = 50
t = 50/15
t = 3{{{1/3}}} hrs or 3 hrs, 20 min
:
Check solution by finding the distance of both, should be equal
Van: 3{{{1/3}}} * 35 = 166{{{2/3}}} miles
Car: 2{{{1/3}}} * 50 = 166{{{2/3}}} miles