A marathoner ran for two days. On the second day he ran at an average

Question

A marathoner ran for two days. On the second day he ran at an average speed of 3 mile 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

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

pandeyashwin · Accepted Answer

The easiest way is to look at the overall average. It's 36/8 = 4.5 mph.
First day's speed is x , second day's would be x+3.

If you look at option A to D , the average is >= the two elements. It not possible for the average to be higher than the two elements

Only in Option E , one element is below the average and another one is above

ScottTargetTestPrep · Answer

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

dave13 · Answer

hi there pandeyashwin

if you say "It not possible for the average to be higher than the two elements" then average is is still higher than 2. pls clarify

.

pandeyashwin · Answer

The average of 1 and 4 will lie between the two extremes. It cannot be higher than 4 or lower than 1.

KHow · Answer

Can someone please help in understanding the concepts with this one? I am getting r=3 but then from there I am having trouble determining that the first day is 2.00. Any help would be appreciated!

Khow

99ramanmehta · Answer

I followed the below approach:

Total distance travelled = 36miles
Let the avg speed on day 1 be x m/hr
=> avg speed on day 2 = (x+3) m/hr

Let the time taken on day 1 be t, hence the time taken on day 2 = (8-t)

applying the simple s*t =d formula

xt + (x+3)(8-t) = 36
=> xt + 8x - xt + 24 - 3t = 36
=> 8x - 3t = 12

Now, from the options, only the value 2 satisfies the above equation as for x = 1.5 m/hr, 't' (for day 1) will have to be equal to 0 which is not the case.

bhupendersingh27 · Answer

alternate to average speed method, we can also try answer options

first take option c : 
Speed on first day: 1 mph
Speed on second day: 1+3 = 4 mph

D=36 miles
with above speed total time can not be 8 hours, as if we assume he runs at highest speed i..e 4 mph on both day then also total time will be 36/4= 9 hours.

so option C not possible

Similarly consider option D
1st day speed: 1.5 MPH
2nd Day speed: 4.5 MPH

try calculating total time considering greater speed i.e. 4.5 hrs, we are getting 8 hours, but again it is not possible as it will mean that he has not run on 1st day, and first day speed would be Zero. so this option isn't possible.

Option E: 
1st day speed: 2 mph
2nd day speed: 4 mph

total time of 8 hours is possible with these speeds. 1st day 6 miles 3 hours, and second day 30 miles 5 hours, total 8 hours.

Answer is Option E

pappal · Answer

i tried this way,
let he ran m miles at the average speed of s mph on day 1
and 36-m miles at the average speed of s+3 mph on day 2
now using the average speed formula
36/8=36/{m/s + (36-m)/(s+3)}
3m+36s=8s^2+24s
3m=8s^2-12s
since 3*m is always a positive quantity 
the only value of s that gives a positive value of 3m is s=2 mph (rest all given values result in either zero or negative)
E

Kinshook · Answer

A marathoner ran for two days. On the second day he ran at an average speed of 3 mile 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?

Let the average speed on first day be x miles/hour.
The average speed on second day = (x + 3) miles/hour

Let the time he ran on first day be t hours
The time he ran on second day = 8-t hours

Total distance for 2 days = 36 miles = xt + (x+3)(8-t) = xt + 24 - xt -3t + 8x = 24 + 8x - 3t = 36; 
8x - 3t = 12
x = (12+3t)/8 = 3(4+t)/8; where 0<t<8

1.5 < x < 4.5

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

x = 2

IMO E

Adit_ · Answer

Avg speed is a game of how much time is spent in doing something.

Take extremes and check:
All 8 hours spent into the avg speed of 2nd day:
8x=36
x=4.5
But we know this way that first day is 1.5mph and he DID run
x has to be greater than 4.5
and when that happens, 1st day becomes>1.5
Hence 2 is the only option.

Answer:  Option E

A marathoner ran for two days. On the second day he ran at an average

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

A marathoner ran for two days. On the second day he ran at an average

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards