A cyclist bikes x distance at 10 miles per hour and returns

Question

A cyclist bikes x distance at 10 miles per hour and returns over the same path at 8 miles per hour. What is the cyclist's average rate for the round trip in miles per hour?

A. 8.1 
B. 8.3 
C. 8.6 
D. 8.9 
E. 9.0

Bunuel · Accepted Answer

Let the distance be 40 miles (40 because it's divisible by 10 and 8)

Time for 1st trip=40/10=4 hours
Time back =40/8=5hours

Average rate=total distance/total time=(40+40)/(4+5)=80/9=8.9

D.

It's possible to write the formula with variable x for distance but the above way is fastest.

Here is the formula if you need it:
Av rate=(x+x)/(x/10+x/8)=80/9=8.9

Jamico7 · Answer

total distance = 2x
Time on the way there is (x miles)/(10 miles/hour)= x/10 hours
Time on the way back is (x miles)/(8 miles/hour)= x/8 hours
Total time=(x/10)+(x/8)=(9x/40) hours

Average rate=(total distance)/(total time)
x is a dummy variable and will cancel out
Average rate=(2x)miles/(9x/40)hour= 80/9 mph=8.9 mph D

hogann · Answer

Pick numbers that make sense. 8x10--> 80 miles

1st Trip takes 8 hours at 10/mph
2nd Trip takes 10 hours at 8/mph

160/18
= 8.9mph

zachman · Answer

Another approach to roundtrip average rates is to conceptually utilize weighting. Because time is a weight here, slightly more time, or weight, is used at 8 mph than 10 mph, so the average rate should be slightly closer to 8 mph than it is to 10 mph. Answer 8.9 mph.

Phew...I finally made my first post.

Phew...I finally made my first post.

ravsg · Answer

the avg speed formula does the trick ...

subhashghosh · Answer

2x/(x/10 + x/8)

= 2/(1/10 + 1/8)

= 2 * 40/(4 + 5)

= 80/9 = 8.88 ~ 8.9

Answer - D

menacel · Answer

Substitute a number in for X

RT=D

R T D
 --------------------------------
a 10 40
b 8 40

I chose the common multiple 40, so now since average rate = total distance/total time we need to find time

rt=d --? t=d/4

so

R T D
 --------------------------------
a 10 4 40
b 8 5 40
---------------------------------------
total 9 80

r=80/9

r=8.888888 --> ~8.9 so D is the answer

Abhishek009 · Answer

Let x = 40 ( LCM of 10 & 8 )

So, Time taken for onward journey = 4 hrs
And, Time taken for return journey = 5 hrs

So, total time taken = 9 hrs

Hence, average speed = 2*40/9 => 8.89 Hrs
  
Thus, answer will be (D) 8.9 hours..

shravan2025 · Answer

the best way to solve avg speed when same distance is convered by two dift velocity

Avg speed = 2ab/a+b

so 2x10x8/18 =8.9 so answer is D

ScottTargetTestPrep · Answer

We can use the formula average speed = total distance/total time. Since the distance for each leg traveled is x, the total distance is 2x, the time going is x/10, and the time coming back is x/8. We have:

average = 2x/(x/10 + x/8)

average = 2x/(4x/40 + 5x/40)

average = 2x/(9x/40)

average = (2x)(40/9x)

average = 80/9 = 8.9

Answer: D

Nunuboy1994 · Answer

This is clearly a round trip question so we should consider the formula

Total Distance= AvgSpeed * Time Spent

And also that

Distance1= Distance2 (we hold the distance constant because of course the distance on each trip is obviously the same)

Now we can just plug in a simple value

40/8 = 5 hours

40/10= 4 hours

80miles= Avgspeed * 9 hours

80/9= 8.888888 so round up

D

Abhishek009 · Answer

\frac{2*10*8}{(10+8)} = 8.8888...  ~  8.9  , Answer must be (D)

vaani03 · Answer

There's an easy way to do Round Trip questions, which has helped a lot:

Avg speed = 2 * Speed1 * Speed2 / Speed1 + Speed 2
2*10*8/10+2
160/18
80/9
8.9 // Ans D

A cyclist bikes x distance at 10 miles per hour and returns

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

A cyclist bikes x distance at 10 miles per hour and returns

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