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Car A started driving north from point X traveling at a cons
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06 Jul 2018, 16:21
06 Jul 2018, 16:21
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Question Stats:
57% (02:21) correct
42% (02:19) wrong based on 98 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
(A) 30
(B) 60
(C) 90
(D) 120
(E) 150
Re: Car A started driving north from point X traveling at a cons
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07 Jul 2018, 22:50
07 Jul 2018, 22:50
6
From question,
Each car is supplied with 8 gallons of fuel. A gallon of fuel is good for 30 miles.
Therefore, with 8 gallons total distance that could be covered before completely exhausting the fuel is 30 * 8 = 240 miles.
Car A can travel at a rate of 40 miles per hr. Hence, if car A travels 240 miles at a speed of 40 miles per hr. It will take a total of \(240/40 = 6\) hrs to do this.
Car B started 1 hr late than Car A in moving at the same direction. Hence car B traveled only \(5\) hrs when car A ran out of fuel.
In 5 hrs car B covered a distance of \(30 * 5 = 150\) miles.
Hence the difference between the distances covered by A and B would be \(240 - 150 = 90 miles.\)
Each car is supplied with 8 gallons of fuel. A gallon of fuel is good for 30 miles.
Therefore, with 8 gallons total distance that could be covered before completely exhausting the fuel is 30 * 8 = 240 miles.
Car A can travel at a rate of 40 miles per hr. Hence, if car A travels 240 miles at a speed of 40 miles per hr. It will take a total of \(240/40 = 6\) hrs to do this.
Car B started 1 hr late than Car A in moving at the same direction. Hence car B traveled only \(5\) hrs when car A ran out of fuel.
In 5 hrs car B covered a distance of \(30 * 5 = 150\) miles.
Hence the difference between the distances covered by A and B would be \(240 - 150 = 90 miles.\)
General Discussion
Re: Car A started driving north from point X traveling at a cons
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10 Jul 2018, 06:14
10 Jul 2018, 06:14
1
Expert Reply
Explanation
The question asks (indirectly) how far the two cars traveled, as those distances are necessary to find the distance between them. Since the cars go in the same direction, the skeleton equation is as follows:
Car A’s distance – Car B’s distance = Distance between cars
All distances refer to the time when car A ran out of fuel.
Since the limiting factor in this case is A’s fuel supply, calculate how far the car is able to drive before running out of fuel. This in itself is a rate problem of sorts:
30 miles per gallon × 8 gallons = 240 miles
So car A will end up 240 miles north of its starting point, which happens 240 ÷ 40 = 6 hours after it started. What about car B? It started an hour later and thus traveled (30 miles per hour)(6 hours – 1 hour) = 150 miles by that time.
Therefore, the two cars were 240 – 150 = 90 miles apart when car A ran out of fuel.
The question asks (indirectly) how far the two cars traveled, as those distances are necessary to find the distance between them. Since the cars go in the same direction, the skeleton equation is as follows:
Car A’s distance – Car B’s distance = Distance between cars
All distances refer to the time when car A ran out of fuel.
Since the limiting factor in this case is A’s fuel supply, calculate how far the car is able to drive before running out of fuel. This in itself is a rate problem of sorts:
30 miles per gallon × 8 gallons = 240 miles
So car A will end up 240 miles north of its starting point, which happens 240 ÷ 40 = 6 hours after it started. What about car B? It started an hour later and thus traveled (30 miles per hour)(6 hours – 1 hour) = 150 miles by that time.
Therefore, the two cars were 240 – 150 = 90 miles apart when car A ran out of fuel.
