Problem Solving

aaron1981 wrote:A marathoner ran for two days. On the second day, he ran at an average speed of 3 miles per hour faster than he ran on the first day. If during the two days he ran a total of 36 miles and did a total of 8 hours running, which of the following could be his average speed, in miles per hour, on the first day?

(A) 0.25
(B) 0.50
(C) 1.00
(D) 1.50
(E) 2.00

OA E

Let the marathoner's speed on the first day be x miles per hour.

Thus, his speed on the second day was „(x ‚+ 3)… miles per hour.

Let the time for which the marathoner ran on the first day be t hours.

Thus, the time for which he ran on the second day ƒ „(8 - t)… hours.

Distance covered by him on the first day = „x *t… miles.

Distance covered by him on the second day = („„x ‚+ 3)*…(8 - t)…… miles.

Thus, total distance covered in two days = [†xt ‚+ („„x ‚+ 3)*…(8 - t)]…‡ miles.

Thus, we have:

xt ‚+ („„x ‚+ 3)*…(8 - t) = ƒ 36
=ƒ> xt ‚+ 8x - xt ‚ + 24 - 3t ƒ= 36
ƒ=> 8x ƒ= 3t ‚+ 12

Since this is a single linear equation with two variables, we cannot get the unique value of x;
however, we can get consistent values of x.

Working with the options one at a time:

Option A: x = 0.25 ƒ=> t ƒ= -10/3 -- Not possible, since t cannot be negative.

We see that since this is a 'Could be the value' type of question and that the smallest
option value of x yields a negative value for t, thus we should first try the largest value of x.

Option E: x ƒ= 2 ƒ=> t ƒ= 4/3 - Possible

Thus, we have x ƒ= 2. We need not check other options as the only option must be correct.

The correct answer: E

Hope this helps!

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-Jay
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aaron1981 wrote:A marathoner ran for two days. On the second day, he ran at an average speed of 3 miles per hour faster than he ran on the first day. If during the two days he ran a total of 36 miles and did a total of 8 hours running, which of the following could be his average speed, in miles per hour, on the first day?

(A) 0.25
(B) 0.50
(C) 1.00
(D) 1.50
(E) 2.00

OA E

Let us see this question from another approach.

Average speed of the marathoner for the two days ƒ= (Total distance) / (Total time) = 36/8 = 4.5 miles per hour

Say the average speed on the first day be x miles per hour, thus, the average speed on the second day
would be „(x +‚ 3)… miles per hour

Thus, the average speed of 4.5 miles per hour must lie between the values of the speeds on the two days.

Thus, we have:

x < 4.5 < x ‚+ 3

Among the options, only x ƒ= 2 satisfies.

The correct answer: E

Hope this helps!

Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Bangkok | Abu Dhabi | Rome | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

aaron1981 wrote: ↑

Wed Jul 19, 2017 12:49 am

A marathoner ran for two days. On the second day, he ran at an average speed of 3 miles per hour faster than he ran on the first day. If during the two days he ran a total of 36 miles and did a total of 8 hours running, which of the following could be his average speed, in miles per hour, on the first day?

(A) 0.25
(B) 0.50
(C) 1.00
(D) 1.50
(E) 2.00

OA E

The average speed for the entire two days was 36/8 = 4.5 mph

Thus, since the speed on the first day was 3 mph slower than that of the second day, the speed on the first day must be less than 4.5 mph and the speed on the second day must be greater than 4.5 mph.

Since the speed on the second day is greater than 4.5 mph, which is 3 mph faster than that of the first day, the speed on the first day must be greater than 1.5 mph. So the only possible speed on the first day, from the given answer choices, is 2 mph.

Answer: E