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

Hi iamwfy,

we can conclude the above thing fast.......

At 50mph truck needs 1 gallon for 20 miles.
At 60mph truck needs 1.3gallons for the same 20 miles(bcoz the consumption is 30%higher)

It has to travel 160 miles at 60mph,so it will need 1.3 x 8 =10.4 gallons.
Since it has only 10 gallons it has to wait for 20 minutes to get the extra 0.4 gallon.

So total time is 160minutes +20 minutes = 180

@60 mph mileage = (1 - 0.3) * 20 = 14 mpg

Time = Distance/speed
TIme = 160/60 hours
Time = 160/60 * 60 minutes
Time = 160 minutes.
Since the truck is using gas at the rate of 14 mpg and there are only 10 gallons. So,

Time = 160 + 20 = 180.

ANSWER: B

To travel 160 miles with 60mph it will obviously take 160 minutes and 20 more minutes to fill the extra gas needed

New mileage @ 60mph = 20/1.3 miles per gallon
Gallons of gas required to cover 160 miles @ 60mph = 160 / (20 / 1.3). But its tank hold only 10 gallons. Hence the truck will make one stop for 20 min.

Normal time to cover 160 miles = 160/60 hr = 160 mins.
Now total time = 160 mins + 20 mins = 180 mins

Sol:
The question is how many times the truck stops for refueling?

If it didn't have to stop; then the truck would travel a distance of 160 m @ 60mph in

160/60 = 2hours 40minutes

Let's see how many times the truck will have to stop for the gas;

@ 60 mph, the mileage of the truck will be;
\(\frac{20}{1.3}\)

So; in 10 gallons; the truck will travel
\(\frac{20*10}{1.3} miles\)
\(\frac{20*10}{1.3} miles \approx 153 miles\)

Still few miles short of 160. Thus; refueling the tank once would suffice even if the tank's capacity is just 10 gallons.

If the truck stopped once for the fill; then it spent an extra 20 minutes.

Total travel time = 2 hour 40 min+20 min = 3 hours = 180 mins

Ans: "B"

Hi Bunuel

Can u clarify, is gallon consumption has to play a vital part to solve it???
I don't think so. Its mentioned to make someone confused...

Rgds
Prasannajeet

We use consumption to see whether 10 gallons are enough to travel 160 miles, so whether 20 additional minutes will be needed to refuel while covering the distance.

Hope it helps.

Hi Bunuel

Understood and thanx for explanation

Rgds
Prasannajeet

The answer is indeed B, but I feel like this question could be made more interesting (or perhaps just harder) if we introduced a choice. The driver can drive at 50 mph or 60 mph. What is the minimum amount of time he could take to reach his destination. Then we'd need to add in 160 miles / 50 mph = 3.2 hours, or 180 minutes + (\(\frac{1}{5} * 60\)) = 192 minutes (not coincidentally answer choice D).

Then we could compare D to B and determine that going 60 mph is faster than 50 and pick B as the overall answer. Of course this might make people think that if he drove at ~55 mph he'd probably get there in under 3 hours without having to refuel.

Just fuel for understanding GMAT algebra concepts!

Thanks!
-Ron

+1.

Thank you Ron for giving me an idea for a question.

The consumption of fuel depends on time or distance, on which one? Please make me clear.

Yes exactly.
I also thought different from everyone.
If travelling at 50 miles/hr - 20 miles/gallon
If travelling at 60 miles/hr (30% more fuel consumption that means 50miles/hr will have 30% more distance) = 20x(10/13).
So it should be made clear in the question.
And then solution becomes critical and answer comes 204 minutes.

Given: 50 mi/hr, gas = 20 mi/hr, 10 gal of gas

1) At 60 mi/hr gas consumption increases by 30% --> (7/10)*20 mi/gal = 14 mi/gal

2) d = 160 mi, so in 10 gals we get 140 mi (this part takes 7/3 hrs) --> 20 mi left

3) then refuel for 20 min, +1/3 hr

4) We still have to cover 20 miles, so 20mi/60 mi/hr = +1/3 hr

5) 7/3 + 1/3 + 1/3 = 9/3 = 3 hours*60 min/1 hr = 180 minutes

Is this a realistic 700 level rates question? The problem is not hard to do but the amount of information makes it time consuming.

60mpg uses 30% more gas
50mph is 20MPG, therefore 60MPG is 70% of that which is 14.

Distance you can go @60mpg on 10 gallons = 14*10 = 140
140/60 = 7/3 = 2hr 20min
Time to wait for gas = 20min
160-140/60 = 20/60 = 1/3 = 20min

2hr 20min+ 20min + 20min = 3hr = 190min

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.