Problem Solving

It took Ellen 6 hours to ride her bike a total distance of 120 miles. For the first part of the trip, her speed was constantly 25 miles per hour. For the second part of her trip, her speed was constantly 15 miles per hour. For how many miles did Ellen travel at 25 miles per hour?

a) 60.00
b) 62.50
c) 66.67
d) 75.00
e) 90.00

Answer is D i.e. 75. See below.

25(t) + 15(6-t) = 120

t = 3

25*3=75

These flavor of questions can be done as mixture problems as well. I find this approach easier to do as it only involves arithmetic and no algebra.

We can get the average speed for her journey = 120/6 = 20 mph

There are two things being mixed here. Journey A = speed of 25 and journey B = speed of 15 .. giving us a mix that is a speed of 20

25......15
....20....
20-15...25-20

5 : 5

1:1
1/2 the journey wrt time was at 25 mph ... 1/2*6 =3
In 3 hrs she went 3*25 = 75 miles

Great explanations guys. The official answer is indeed D. You can view a video explanation here: GMAT video explanation

Used Karishma's method . so, special thnx to her

25/15=5/3

(5/8)*120=75
thats all

Dear experts,

I solved this problem using the Allegation method and correctly came up with 1:1 ratio. However, from there, I assumed that the ratio obtained is that of the distance traveled. Hence, I selected A, which is the wrong answer.

Please advise why is the ratio obtained the ratio of time traveled and not the distance? I would like to solve these problems using allegation rather than weighted average formula. Hence please explain with respect to the allegation concept.

Thanks in advance.

royrijit1 wrote:Dear experts,

I solved this problem using the Allegation method and correctly came up with 1:1 ratio. However, from there, I assumed that the ratio obtained is that of the distance traveled. Hence, I selected A, which is the wrong answer.

Please advise why is the ratio obtained the ratio of time traveled and not the distance? I would like to solve these problems using allegation rather than weighted average formula. Hence please explain with respect to the allegation concept.

Thanks in advance.

Sometimes it's helpful to play around with simple scenarios to get a better feel for a concept.

Say you drive for 1 hour at 10mph and for 1 hour at 20 mph. (So the ratio of time traveled at each speed is 1:1.) You'll drive a total of 30 miles and drive for a total of 2 hours, meaning your average speed is 15 mph, or an equal distance on the number line from both 10 and 20 - a 1:1 ratio.

Now say you drive 20 miles at 10mph and then drive 20 miles at 20mph. This time our distance traveled at each speed is a 1:1 ratio. You'll spend 2 hours driving at 10mph to cover 20 miles and 1 hour driving at 20 mph to cover 20 miles. You'll drive a total of 40 miles and spend a total of 3 hours driving, giving you an average speed of 40/3 = 13.3333... Now the average speed is closer to 10 than 20 - not a 1:1 ratio. This makes sense as you'd spend more time driving at the slower speed, thus weighting your average towards this end.

So when you're using alligation in a ratio question, the ratio gives you the ratio of the amount of time spent traveling at each respective speed, not the ratio of the distances covered at each speed.