A moving van starts out from a house at 8 a.m., traveling at an averag

Question

A moving van starts out from a house at 8 a.m., traveling at an average speed of 50 miles per hour. One hour and 30 minutes later a car starts out from the same house traveling in the same direction as the van at an average speed of 70 miles per hour. If both vehicles continue at their respective average speeds without making any stops, at what clock time will the car overtake the van?

(A) 9:30 a.m.
(B) 10:30 a.m.
(C) 10:45 a.m.
(D) 11:45 a.m.
(E) 1:15 p.m.

(A) 9:30 a.m.
(B) 10:30 a.m.
(C) 10:45 a.m.
(D) 11:45 a.m.
(E) 1:15 p.m.

D3N0 · Answer

Ans: E
Van travelling at 50miles/hr will travel 75 miles in 1hr 30 min. then Car starts at 70miles per hrs. at this point distance between them at 9:30 am is 75 miles and covering speed of car is 20 miles/hr by this it will take 3hrs 45min for car to cross the Van and time will be 9:30 am + 3hr45min= 1:15PM

mskx · Answer

Start 8:00 - 1:30hrs later -> 9:30

1: Distance Van = 50*1,5 = 75 miles
2: 50x+75 = 70x 
x=3 3/4

9:30 + 3 3/4
Hence, 1:15pm  E

bharat9995 · Answer

Van Starts at 8:00 am. Free Run for 1.30 hrs......distance covered--->50mph*1.5=75 miles
Car Starts at 9:30am. Now distance between Van and Car is 75 miles.
Distance covered by car every hour is 20miles....-> 75 miles will be covered in 75/20=3.75 hours
Which implies 9.30 am plus 3.75 hours, car crosses the van  1.15pm.

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zishu912 · Answer

In the first one hour and thirty minutes, Van covers a total distance of = 50 + 25= 75km

=> Van is having a lead of 75 km, at 9:30, car left from the same place and it has to cover the lead of 75 km taken by Van
So this lead will be covered in 75/(70 - 50)= 75/20 = 15/4 = 3 hr 45 minutes

(70 - 50) is the relative speed of the car and van and both of them are running in same direction

so the car will over take the van after 3 hr and 45 minutes after it starts at 9:30

Hence the correct answer will be E 1:15 p.m.

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generis · Answer

In this "catch-up" problem, solve for the "gap" distance between vehicles (distance is created by the van traveling alone for 1.5 hours). Find time taken. Add to start time of car.

1) DISTANCE = gap created by the moving van, which starts first.   D = r*t  
  D   created by van:   50 mph*\frac{3}{2}hrs=75   miles

2) RATE at which the gap closes = relative speed
Same direction of travel. To find rate at which gap closes, subtract speeds
Van = 50 mph, and Car = 70 mph
Relative speed: (70 mph - 50 mph) = 20 mph

3) TIME needed to close the gap? How many hours will it take for the car to catch the van?   Time = \frac{D}{r} 
 T = \frac{75mi}{20mph}=3\frac{15}{20}=3\frac{45}{60}   hours

Time taken to close the gap: 3 hours, 45 minutes

4) CLOCK TIME at which car overtakes van?
Use the start time of the second vehicle, the car

CAR leaves at 9:30 a.m. (1 \frac{1}{2}  hours after van)

Car catches van at (9:30 a.m. + 3 hrs, 45 mins) = 1:15 p.m.

Answer E

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A moving van starts out from a house at 8 a.m., traveling at an averag

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