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# Car A started driving north from point X traveling at a constant rate

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Math Expert
Joined: 02 Sep 2009
Posts: 48044
Car A started driving north from point X traveling at a constant rate  [#permalink]

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08 Jul 2018, 21:36
00:00

Difficulty:

65% (hard)

Question Stats:

58% (02:32) correct 42% (02:24) wrong based on 66 sessions

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Car A started driving north from point X traveling at a constant rate of 40 miles per hour. One hour later, car B started driving north from point X at a constant rate of 30 miles per hour. Neither car changed direction of travel. If each car started with 8 gallons of fuel, which is consumed at a rate of 30 miles per gallon, how many miles apart were the two cars when car A ran out of fuel?

(A) 30
(B) 60
(C) 90
(D) 120
(E) 150

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Joined: 09 Oct 2015
Posts: 154
Car A started driving north from point X traveling at a constant rate  [#permalink]

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08 Jul 2018, 22:56
car a can travel a max of 240 miles on 8 gallons of fuel.
This will be done in 240/40 hrs, i.e 6 hours

in 6 hours, car b would have traveled 30x5 miles( + 1 hour of being stationary.)

Therefore the ans should be 240 - 150= 90miles
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Joined: 14 Dec 2017
Posts: 455
Re: Car A started driving north from point X traveling at a constant rate  [#permalink]

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08 Jul 2018, 23:58
1
Bunuel wrote:
Car A started driving north from point X traveling at a constant rate of 40 miles per hour. One hour later, car B started driving north from point X at a constant rate of 30 miles per hour. Neither car changed direction of travel. If each car started with 8 gallons of fuel, which is consumed at a rate of 30 miles per gallon, how many miles apart were the two cars when car A ran out of fuel?

(A) 30
(B) 60
(C) 90
(D) 120
(E) 150

Car A can travel a total of = 8*30 = 240 miles before it runs out of fuel

Time taken for Car A to travel 240 miles at a speed of 40 mph = 240/40 = 6 hours

Car B starts from point X, one hour later than Car A, hence it travels for 5 hours.

Distance traveled by Car B in 5 hours at a speed of 30 mph = 5*30 = 150 miles

Hence Distance between Car A & B, when Car A stops = 240 - 150 = 90 miles

Thanks,
GyM
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Joined: 04 Jan 2015
Posts: 1900
Re: Car A started driving north from point X traveling at a constant rate  [#permalink]

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09 Jul 2018, 06:05

Solution

Given:
• Car A started driving north from point X traveling at a constant rate of 40 miles per hour
• One hour later, car B started driving north from point X at a constant rate of 30 miles per hour
• Neither car changed direction of travel
• Each car started with 8 gallons of fuel, which is consumed at a rate of 30 miles per gallon

To find:
• How many miles apart were the two cars when car A ran out of fuel

Approach and Working:
With 8 gallons of fuel,
• Car A can travel for 30 * 8 = 240 miles
• Time taken by car A to travel 240 miles = $$\frac{240}{40}$$ hours = 6 hours

As car B started 1 hour after car A, travel time for car B = 5 hours
• In 5 hours, car B travelled = 5 * 30 = 150 miles
• Therefore, the distance between them = 240 – 150 = 90 miles

Hence, the correct answer is option C.

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Re: Car A started driving north from point X traveling at a constant rate &nbs [#permalink] 09 Jul 2018, 06:05
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