An athlete runs R miles in H hours, then rides a bike Q miles in the

Question

An athlete runs R miles in H hours, then rides a bike Q miles in the same number of hours. Which of the following represents the average speed, in miles per hour, for these two activities combined?

(A) (R-Q)/H
(B) (R-Q)/2H
(C)  /H
(D)  /2H
(E) (R+Q)/2H

Folaa3 · Accepted Answer

Ans is E - R + Q / 2H


formular for avg speed is total distance / total time

Time spent running = H and the time spent biking = H 
total time is H + H = 2H

Total distance is R + Q

Thus E

Praetorian · Answer

Welcome to GMAT Club, w07

Combined distance traveled = R + Q Combined time = H + H ( the athelete runs for H hours and bikes for another H hours) Thus, the combined time = 2H Therefore, Average speed of two activities combined = combined distance / combined time = (R + Q) / (2H) do you see how you get 2H? Praetorian

w07 · Answer

Now I see the 2H, thank you both. Originally I wasn't understanding why it was just over H, but now it makes sense.

mandy · Answer

another E AVERAGE SPEED = TOTAL DISTANCE /TOTAL TIME TOTAL DISTANCE R+Q TOTAL TIME H +H = 2H :wink:

EMPOWERgmatRichC · Answer

Hi All,

As far as story problems go, this one is fairly easy from a "logic" standpoint. You can also solve it by TESTing VALUES.

R = 4
H = 2
Q = 6

So the athlete runs 4 miles in 2 hours, then bikes 6 miles in another 2 hours.

Total Distance = 4+6 = 10 miles
Total Time = 2+2 = 4 hours
Average speed = 10/4 = 2.5 miles/hr.

Plugging these values into the answer choices gives us just one match...

Final Answer:  E

GMAT assassins aren't born, they're made,
Rich

Salvetor · Answer

Rate x Time = Distance
R/H x H = R
Q/H x H = Q

Avg speed = total distance/ total time 
 = (R+Q)/ 2H

JeffTargetTestPrep · Answer

We need to determine average speed:

average speed = total distance/total time

average = (R + Q)/(H + H) = (R + Q)/2H

Answer: E

Nipungupta9081 · Answer

Answer E

For cycle = X * H = R
For Bike = X * H = Q

Average = total distance / total time
= R + Q / 2H

nahid78 · Answer

Distance = R+Q
Time= H+H= 2H
Distance = Time * Speed

YolandaSami · Answer

At first, I interpreted R as a rate (i.e., R mph) and Q as another rate (Q mph), because I saw "miles per hour" in the question and assumed both values were rates. Using this logic, I calculated the average rate as (HR+HQ)/2H = H(R+Q)/2H = R+Q/H which was not part of the given answers. I ended up picking the right answer. However, how do you usually catch this distinction quickly during the test to avoid this kind of mistake?

Bunuel · Answer

The question says the athlete runs  R miles  in H hours, so R is the distance, not the rate. If you wanted the per hour rate, it would be distance/time = R/H miles per hour. Same for biking: Q is the distance, and the biking rate would be Q/H miles per hour.

So whenever you see something like “runs R miles in H hours,” treat R as distance. Watch the units closely. If it doesn't say “R miles  per hour ,” then R is not a per hour rate.

An athlete runs R miles in H hours, then rides a bike Q miles in the

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An athlete runs R miles in H hours, then rides a bike Q miles in the

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