Lexy walks 5 miles from point A to point B in one hour, then

Lexy walks 5 miles from point A to point B in one hour, then bicycles back to point A along the same route at 15 miles per hour. Ben makes the same round trip, but does so at half of Lexy’s average speed. How many minutes does Ben spend on his round trip?

Average speed = total distance/total time

We know the total distance is 5+5 (going from A to B then from B to A)

Time = distance/speed
Time = 5/15
Time = 1/3 hour

Average speed = (10)/(1hr + 1/3hr)
Average speed (lexi) = 10 / 1.33
Therefore, if Ben's average speed is 1/2 of lexi's then his speed = 10/2.66.

This means it took him 2.66 hours to cover the same 10 miles Lexi did. 2.66 hours = roughly 160 minutes.

Answer: D). 160

Lexy travels 10 miles (5+5) in 80 Mins (60 + 60/3)
So, speed of Lexy = 10/80 = 1/8

Speed of Ben is half of speed of Lexy = 1/16

So, time taken by Ben = 10 / (1/16) = 160 Minutes

Answer = D

Hi Bunuel,

Can u tell me why we can't use this formula?

Avg speed=2ab/a+b

Thanks in advance

Total time taken by Ben will be twice the total time taken by Lexy
ie from 2 * ( 1+15/5) = 2* ( 4/3) = 8/3 hours = 8*60/3 minutes = 160 minutes

Harmonic average for average speed: 2/(1/5+1/15)=15/2

the half speed: 15/2:2=15/4

10/(15/4)=8/3h*60=160min.

D

Time taken by Lexy to walk from point B to A => 60*5/15 = 20 mins.

Average speed of Lexy = 5+5/(60+20) = 10/80 = 7.5 mph.

Ben's average speed = 7.5/2 = 3.75 mph.

Time taken by Ben = 10*60/3.75 = 160 mins. Ans (D).

1/2 of Lexy's average speed is Ben's speed..

1/2(2ab/a+b)
=1/2*{(2*15*5)/15+5)}
=3.75..

We need the time in minutes so Total dis/Total time=Average speed

10/x=3.75/60
Therefore, x=160 minutes

Lexy Avg speed: (5+5)/(1+1/3)=7.5
ben's speed : 7.5/2
time taken by ben: (10*2/7.5)*60=160 mins

Lexy Avg speed: (5+5)/(1+1/3)=7.5
ben's speed : 7.5/2
time taken by ben: (10*2/7.5)*60=160 mins

OFFICIAL EXPLANATION:


We begin by figuring out Lexy’s average speed. On her way from A to B, she travels 5 miles in one hour, so her speed is 5 miles per hour. On her way back from B to A, she travels the same 5 miles at 15 miles per hour. Her average speed for the round trip is NOT simply the average of these two speeds. Rather, her average speed must be computed using the formula RT = D, where R is rate, T is time and D is distance. Her average speed for the whole trip is the total distance of her trip divided by the total time of her trip.

We already know that she spends 1 hour going from A to B. When she returns from B to A, Lexy travels 5 miles at a rate of 15 miles per hour, so our formula tells us that 15 T = 5, or T = 1/3. In other words, it only takes Lexy 1/3 of an hour, or 20 minutes, to return from B to A. Her total distance traveled for the round trip is 5+5=10 miles and her total time is 1+1/3=4/3 of an hour, or 80 minutes.

We have to give our final answer in minutes, so it makes sense to find Lexy's average rate in miles per minute, rather than miles per hour. 10 miles / 80 minutes = 1/8 miles per minute. This is Lexy's average rate.

We are told that Ben's rate is half of Lexy's, so he must be traveling at 1/16 miles per minute. He also travels a total of 10 miles, so (1/16) T = 10, or T = 160. Ben's round trip takes 160 minutes.

Alternatively, we could use a shortcut for the last part of this problem. We know that Ben's rate is half of Lexy's average rate. This means that, for the entire trip, Ben will take twice as long as Lexy to travel the same distance. Once we determine that Lexy will take 80 minutes to complete the round trip, we can double the figure to get Ben's time. 80 × 2 = 160.

The correct answer is D.



Please give kudos if this was helpful in any way!

average speed = total distance / total time

Lexy travels a total of 10 miles and spends 80 minutes doing so.

Lexy's speed = 10 / 1 + 1/3 = 30/4 = 7.5

Ben's speed = 7.5 / 2 = 3.75

Ben's time = 10/3.75 * 60 = 160

Answer is D.

hey , thanks for the explanation :
so what i did is Time =total distance / avg.speed
that is 15/4 miles/hours so i converted miles/hour into miles/min here only and getting 225miles/min.
now , T=10/225 . i am getting some weird answer in decimal can you please suggest the way i have done is it wrong??
can we do that way ??

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