Tammy bikes the course of a race at 30 miles per hour, then returns ho

Question

Tammy bikes the course of a race at 30 miles per hour, then returns home along the same route at 10 miles per hour. If the total time it takes her to travel the course and return home is 2 hours, and if the time spent turning around is negligible, what is the length, in miles, of the race course?

A) 15
B) 20
C) 25
D) 30
E) 35

A) 15
B) 20
C) 25
D) 30
E) 35

Nidzo · Answer

Let the distance of the course = d
Let the time it takes Tammy the course the first time = t

First time doing the course:  
Speed = 30
Time = t
Distance = d

Formula for distance is  Distance = Speed * Time

Which gives us:  d = 30t

Return Trip: 
Speed = 10
Time = 2-t
Distance = d

Once again using the distance formula, we get:  d = 10(2-t)

d = 20 - 10t  multiply through by 3

3d = 60 - 30t

Subbing in  d = 30t  into  3d = 60 - 30t  gives us:

3d = 60 - d

4d = 60

d = 15

Answer A

Abhishek009 · Answer

2\frac{(10*30)}{(30+10)} = \frac{300}{20} = 15 , Answer will be (A)

tenben · Answer

Abhishek009  Sir, How are you arriving at this formula?

Abhishek009 · Answer

No Sir, Please, I am just a fellow aspirant like U...

Its actually a shortcut formula

D = 2\frac{s_1s_2}{(s_1+s_2)}

Hope this resolves your query !!!

e3thekid · Answer

The two distances are equal to each other in a round-trip question. We know the entire trip took 2 hours to complete, so we can assign t for time of trip one, and (2-t) for the second trip back home.

R x T = D

Trip 1: 30 x t = 30t
Trip 2: 10 x (2-t) = 20 - 2t

Distance trip 1 = Distance trip 2

30t = 20 - 2t
32t = 20
 t = 20/32 = 5/8

Distance of race course: (plug t back into either distances)

30t = 30(5/8) —> 60/4 —> 15 miles

Option A

Posted from my mobile device

Rance14 · Answer

A ------------------- B

let distance btw A-B = D miles

from A-B 
S1=30mi/hr
Distance = D miles
T1=D/30

from B-A
S2=10mi/hr
Distance = D miles
T2=D/10

Total time = D/30+D/10
also given total time takes = 2 hrs

D/30+D/10=2
4D=60
D=15 miles

ThickGuitar · Answer

the ratio of the speeds is 30:10 which simplifies to 3:1,

that means the ratio of the times is therefore 1:3 , total ratio is 4

whole trip takes 2 hours, 
Calculating the times: 
Racecourse): time to cover 30miles = 1/4 (2hours) = 1/2hour or 30mins
(Back home): time to cover 10 miles = 3/4 (2hours) = 1.5 hours or 90mins  (in the actual gmat, for the sack of saving time, you don't actually have to calculate the distance back home because the question asked for the length of the race course only).

that means at 30mph, Tammy took 1/2hr to cover distance of the actual race course.

30 miles : 1hr
1/2hr is 15 miles (Answer D)

The reason we do not include the distance covered when Tammy was travelling at 10mph is because that is the return trip home. It's similar logic to saying, the distance from your house to the mall is 3km. Going to and from the mall means you actually cover a distance of 6km, but that does not mean the mall is 6km away from homw, it is still 3km but because it's a round trip, you cover double the distance.

Tammy bikes the course of a race at 30 miles per hour, then returns ho

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

Tammy bikes the course of a race at 30 miles per hour, then returns ho

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