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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