Bob bikes

Third option

let us say distance b/w home and school is 2s


s/x + s/y = t
s(x+y)/xy = t
s = xyt/(x+y)


distance b/w home and school = 2s = 2xyt/(x+y)

GmatKiss wrote:Bob bikes to school every day at a steady rate of x miles per hour. On a particular day, Bob had a flat tire exactly halfway to school. He immediately started walking to school at a steady pace of y miles per hour. He arrived at school exactly t hours after leaving his home. How many miles is it from the school to Bob's home?

(x + y) / t

2(x + t) / xy

2xyt / (x + y)

2(x + y + t) / xy

x(y + t) + y(x + t)

pls explain in detail

Let the distance to school = 20 miles.
Let x = 5 miles per hour.
Time spent biking = 10/5 = 2 hours.
Let y = 2 miles per hour.
Time spent walking = 10/2 = 5 hours.
Total time = t = 2+5 = 7.
The questions asks for the total distance: 20 miles. This is our target.

New we plug x=5, y=2, and t=7 into the answers to see which yields our target of 20.

Only answer choice C works:
2xyt/(x+y) = (2*5*2*7)/(5+2) = 140/7 = 20.

The correct answer is C.

Hey guys ,

I initially took 5 minutes ( without looking at the answer options ) and was not able to come up with a good answer . Then I totally left that approach and looked at the answer options . While looking at the answer options I just kept in mind that the right option should have something in the form of D = ST .In other words it should not have x +t or (x+y )/t ==> S/T???!! or some thing like that ( as it does not make sense ) . With that in mind I could immediately eliminate A,B,D,E . It took me approx. 40 sec without using pen/paper . I know it may not work if more than option was in the proper format but still thought it was worth while sharing this approach.

atnt444 wrote:Hey guys ,

I initially took 5 minutes ( without looking at the answer options ) and was not able to come up with a good answer . Then it totally left that approach and looked at the answer options . While looking at the answer options I just kept in mind that the right option should have something in the form of D = ST .In other words it should not have x +t or (s+y )/t ==> S/T or some thing like that ( as it does not make sense ) . With that in mind I could immediately eliminate A,B,D,E . It took me approx. 40 sec without using pen/paper . I know it may not work if the options we in the proper format but still thought it was worth while sharing this approach.

Nice!!!

During the real GMAT, your approach is actually how this ques is meant to be dealt.

Thnx for sharing