SOLUTION: A truck and a car driving uniformly from city A to city B. The truck leaves at 9:15A.M and arrives at 1:15P.M. The car leaves at 10:00A.M and arrives at 12:45P.M. At what time does

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Question 803349: A truck and a car driving uniformly from city A to city B. The truck leaves at 9:15A.M and arrives at 1:15P.M. The car leaves at 10:00A.M and arrives at 12:45P.M. At what time does the car overtake the truck?
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
A truck and a car driving uniformly from city A to city B.
The truck leaves at 9:15A.M and arrives at 1:15P.M.
The car leaves at 10:00A.M and arrives at 12:45P.M.
At what time does the car overtake the truck?
:
:
Truck took 4 hrs to make the trip, Car took 2.75 hrs
:
Let d = dist from A to B
:
Find the speed of the two vehicles (speed = dist/time)
= speed of truck
= speed of the car
:
let t = time for the car to overtake the truck
The truck leaves 45 min before the car, therefore
(t+.75) = travel time of the truck
:
When the car overtakes the truck they will have traveled the same distance.
Write a distance equation dist = speed *time
Car dist = truck dist
t = (t+.75)
CRoss multiply
4dt = 2.75d(t+.75)
4dt = 2.75dt + 2.0625d
get rid of d, divide eq by d
4t = 2.75t + 2.0625
4t - 2.75t = 2.0625
1.25t = 2.0625
t = 2.0625/1.25
t = 1.65 hrs for the car to overtake the truck
Which is 1 + .65(60) = 1 hr 39 min
The car overtakes the truck at: 10:00 + 1:39 = 11:39 AM
:
:
See if they travel the same distance in that time
Assume the A-B distance is 200 mi
then
= 50 mph is the truck speed
and
= 72.7 mph is the car speed
:
Find the distances
Truck 50(1.65+.75) = 120 mi
Car: 72.7(1.65) ~ 120 mi; confirms our solution