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When a truck travels at 60 miles per hour, it uses 30 percent more gas

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When a truck travels at 60 miles per hour, it uses 30 percent more gas [#permalink]

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New post 02 Nov 2017, 23:06
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When a truck travels at 60 miles per hour, it uses 30 percent more gasoline to travel any distance than it does when it travels at 50 miles per hour. The truck can travel 20 miles on a gallon of gas if it is traveling at 50 miles per hour. The truck has only 10 gallons of gas and is 160 miles from its destination. It takes 20 minutes for the truck to stop for gas. How long will it take the truck to reach its final destination if it is driven at 60 miles per hour?

(A) 160 minutes
(B) 180 minutes
(C) 190 minutes
(D) 192 minutes
(E) 195 minutes
[Reveal] Spoiler: OA

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Re: When a truck travels at 60 miles per hour, it uses 30 percent more gas [#permalink]

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New post 02 Nov 2017, 23:50
Bunuel wrote:
When a truck travels at 60 miles per hour, it uses 30 percent more gasoline to travel any distance than it does when it travels at 50 miles per hour. The truck can travel 20 miles on a gallon of gas if it is traveling at 50 miles per hour. The truck has only 10 gallons of gas and is 160 miles from its destination. It takes 20 minutes for the truck to stop for gas. How long will it take the truck to reach its final destination if it is driven at 60 miles per hour?

(A) 160 minutes
(B) 180 minutes
(C) 190 minutes
(D) 192 minutes
(E) 195 minutes


Speed = 50 miles/Hr ; Gasoline usage = 1 gallon/20 miles
Speed = 60 miles/Hr ; Gasoline usage = 1.3 gallon/20 miles
Total Stock of Gasoline = 10 gallons
Till 120 miles; D travelled = 120 miles; Speed = 60 miles/Hr; Gasoline Used = 7.8 gallons (2.2 left) ; time taken = 2 hrs
Till 140 miles; D travelled = 140 miles; Speed = 60 miles/Hr; Gasoline Used = 9.1 gallons (0.9) ; time taken = 140 mins
Stop for Gasoline = 20 mins ; time taken = 160 mins
Till 160 miles; D travelled = 160 miles; Speed = 60 miles/Hr; time taken = 160+20 mins = 180 mins (20 mins to travel 20 miles)
B
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Re: When a truck travels at 60 miles per hour, it uses 30 percent more gas [#permalink]

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New post 03 Nov 2017, 02:50
60 m/h - 1,3 gasoline gallons for every 20 miles
50 m/h - 1 gasoline gallon for every 20 miles
We have 10 gallons left, so 10/1.3~7,7 rounding to units = 7; 7*1,3=9,1 gallons, so we have 0,9 gallons left.
7*20 miles=140miles, which means that with speed 60m/h it would take 140 mins, however we need to refuel to cover remaining 20 miles. Thus, after refuelling it would take 20 min more to cover 20 miles ==> 140+ 20=180 mins. Answer B.

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When a truck travels at 60 miles per hour, it uses 30 percent more gas [#permalink]

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Bunuel wrote:
When a truck travels at 60 miles per hour, it uses 30 percent more gasoline to travel any distance than it does when it travels at 50 miles per hour. The truck can travel 20 miles on a gallon of gas if it is traveling at 50 miles per hour. The truck has only 10 gallons of gas and is 160 miles from its destination. It takes 20 minutes for the truck to stop for gas. How long will it take the truck to reach its final destination if it is driven at 60 miles per hour?

(A) 160 minutes
(B) 180 minutes
(C) 190 minutes
(D) 192 minutes
(E) 195 minutes

I think the gas information is a lot of extra . . . All you need is to see that he is not going to cover 160 miles with 10 gallons of gas driving at 60 mph. I'm wondering if I have my units confused.

At 50mph, he would be able to go 20 miles/gal * 10 gallons = 200 miles

30 percent fewer miles than that, x = miles he can cover?
\(200 = 1.3x\)
\(x =\frac{200}{1.3}=\)
approx 154 mi

Conclusion: he has to stop for gas.

TIME to travel?

He is 160 miles from his destination. D/r= time

Time to travel, w/o gas stop:
\(\frac{160}{60}=\frac{8}{3} hrs\) without the gas stop

Time for Gas stop = 20 minutes = 1/3 hr

Time total:\(\frac{8}{3} + \frac{1}{3}=\frac{9}{3}= 3 hrs\)

= 180 minutes

Answer B

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Re: When a truck travels at 60 miles per hour, it uses 30 percent more gas [#permalink]

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New post 04 Nov 2017, 01:28
Alexey1989x wrote:
60 m/h - 1,3 gasoline gallons for every 20 miles
50 m/h - 1 gasoline gallon for every 20 miles
We have 10 gallons left, so 10/1.3~7,7 rounding to units = 7; 7*1,3=9,1 gallons, so we have 0,9 gallons left.
7*20 miles=140miles, which means that with speed 60m/h it would take 140 mins, however we need to refuel to cover remaining 20 miles. Thus, after refuelling it would take 20 min more to cover 20 miles ==> 140+ 20=180 mins. Answer B.


Hi Alexey,

You have done a calculation mistake in the portion marked with RED color in your response.

140+ 20=160 not 180
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Re: When a truck travels at 60 miles per hour, it uses 30 percent more gas [#permalink]

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New post 06 Nov 2017, 17:57
Bunuel wrote:
When a truck travels at 60 miles per hour, it uses 30 percent more gasoline to travel any distance than it does when it travels at 50 miles per hour. The truck can travel 20 miles on a gallon of gas if it is traveling at 50 miles per hour. The truck has only 10 gallons of gas and is 160 miles from its destination. It takes 20 minutes for the truck to stop for gas. How long will it take the truck to reach its final destination if it is driven at 60 miles per hour?

(A) 160 minutes
(B) 180 minutes
(C) 190 minutes
(D) 192 minutes
(E) 195 minutes


We are given that when a truck travels at 60 miles per hour, it uses 30 percent more gasoline to travel any distance than it does when it travels at 50 miles per hour, and that the truck can travel 20 miles on a gallon of gas if it is traveling at 50 miles per hour. So, when traveling at 60 mph, the truck travels 20/1.3 = 200/13 miles per gallon of gas.

Thus, the number of gallons of gas used in a 160-mile trip is 160/(200/13) = 160 x 13/200 = 10.4, which is more than the 10 gallons of gas the truck has.

The time to drive 160 miles at 60 mph is 160/60 = 16/6 hours = 8/3 hours x 60 = 160 minutes. However, since we have to stop for 20 minutes to fill the truck with gas (recall that we don’t have a sufficient amount of gas for the trip), the total time for the 160-mile trip is 160 + 20 = 180 minutes.

Answer: B
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Re: When a truck travels at 60 miles per hour, it uses 30 percent more gas   [#permalink] 06 Nov 2017, 17:57
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