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

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Intern
Joined: 07 Jul 2005
Posts: 8
Location: Maryland
An athlete runs R miles in H hours, then rides a bike Q miles in the  [#permalink]

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Updated on: 12 Jan 2015, 00:51
1
6
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Difficulty:

5% (low)

Question Stats:

88% (01:18) correct 12% (01:35) wrong based on 391 sessions

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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) [2(R+Q)]/H
(D) [2(R+Q)]/2H
(E) (R+Q)/2H

Originally posted by w07 on 16 Jul 2005, 07:53.
Last edited by Bunuel on 12 Jan 2015, 00:51, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
Director
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Posts: 713
Re: An athlete runs R miles in H hours, then rides a bike Q miles in the  [#permalink]

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16 Jul 2005, 10:00
2
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
CEO
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Posts: 3223
Re: An athlete runs R miles in H hours, then rides a bike Q miles in the  [#permalink]

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16 Jul 2005, 10:36
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
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Re: An athlete runs R miles in H hours, then rides a bike Q miles in the  [#permalink]

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16 Jul 2005, 15:51
Now I see the 2H, thank you both. Originally I wasn't understanding why it was just over H, but now it makes sense.
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Re: An athlete runs R miles in H hours, then rides a bike Q miles in the  [#permalink]

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17 Jul 2005, 07:57
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w07 wrote:
Last one for now: I will post without the answer so everyone can practice. (Will post answer later.) I apologize if I don't know the proper area of the forum for this, but I need help understanding how to set this up. So if you could all explain your logic, that would be great.

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 mph, for these 2 activities combined?

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

I don't understand the logic behind the choices containing 2H.

another E

AVERAGE SPEED = TOTAL DISTANCE /TOTAL TIME

TOTAL DISTANCE R+Q
TOTAL TIME H +H = 2H

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Re: An athlete runs R miles in H hours, then rides a bike Q miles in the  [#permalink]

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12 Jan 2015, 00:50
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...

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Re: An athlete runs R miles in H hours, then rides a bike Q miles in the  [#permalink]

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09 Feb 2015, 10:30
Rate x Time = Distance
R/H x H = R
Q/H x H = Q

Avg speed = total distance/ total time
= (R+Q)/ 2H
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Re: An athlete runs R miles in H hours, then rides a bike Q miles in the  [#permalink]

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29 Jan 2018, 11:12
w07 wrote:
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) [2(R+Q)]/H
(D) [2(R+Q)]/2H
(E) (R+Q)/2H

We need to determine average speed:

average speed = total distance/total time

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

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Re: An athlete runs R miles in H hours, then rides a bike Q miles in the  [#permalink]

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21 Aug 2019, 07:04
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Re: An athlete runs R miles in H hours, then rides a bike Q miles in the   [#permalink] 21 Aug 2019, 07:04
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