Question

A cyclist notices that her average speed when she has covered exactly half the total distance of her race is 30 km/h. What should her average speed over the second half of the race be if she wants to finish the race with an average speed of 40 km/h?
(a) 45 km/h (b) 50 km/h (c) 60 km/h
(d) 54 km/h
A cyclist notices that her average speed when she has covered exactly half the total distance of her race is 30 km/h. What should her average speed over the second half of the race be if she wants to finish the race with an average speed of 40 km/h?
(a) 45 km/h (b) 50 km/h (c) 60 km/h
(d) 54 km/h
@Mathematics

Answer 1

(30 + 50)/2 = 40....so she needs to go 50 km/h during the second part

Answer 2

Note that it only works out this way because the question stated what her average speed was at exactly the midpoint.

Answer 3

Why divide by 2 ?

Answer 4

Because you're taking the average of the two values...since each of the values represents half of the distance

Answer 5

let the distance be x
now for x/2 distance his speed is 30km/h
so time taken would be x/60 hours
now for average speed of 40km/h his total time is x/40
so other half he has to cover in x/40-x/60 hours
x/120 hours so speed for other half is (x/2)/(x/120)
that is 60 km/h

Answer 6

According to answer key it's 50 km/h

Answer 7

@ash2326, Why would the time taken be x/60 hours ?

Answer 8

for first half the distance is x/2 km
and average speed is 30km/h
so time =distance/average speed

Answer 9

But in second half, average speed changes

Answer 10

ya, i've calculated it only for first half

Answer 11

You can also think of it this way:

A course contains 2 exams. You got a 30 on your first exam...what do you need get on your second exam to have a 40 average? 50. I think ash is overcomplicating this one :)

Answer 12

i've checked it should be 60

Answer 13

checked where?

Answer 14

I think storm fire is right.

Answer 15

i took a n example suppose the total distance is 120km
so first half is covered in 2 hours (60km/30km/h)
now if i take average speed 60km/h for second half it takes 1 hour
total time 3 hours
so average speed 40km/h

Answer 16

I too did with this same example and got 60 km/h. But I think it's wrong.

Answer 17

if u take 50 km/h for second half it will take 1.2 hours for second half
total time would be 3.2 hours
in that case average speed is 37.5kmph

Answer 18

i tried taking another example of 100km also it's also giving average speed for second half 60km/h

Answer 19

The distance is irrelevant here. In my mind, it's simply an equation:
\[\frac{30km/h}{2} + \frac{50km/h}{2}=40km/h\]

Answer 20

yeah the distance is irrelevant i took x and got 60km/h

Answer 21

hmm

Answer 22

I do see your point. I guess it boils down to whether he should follow the answer key or go with 60km/h :)

Answer 23

Ok, I'm sold on 60 km/h...I guess I oversimplified it.

Answer 24

\[t=\frac{d}{r} \]Let d be the total race distance and r be the required speed to effect an average speed of km/h. Solve the following for r:\[\frac{d/2}{30}+\frac{d/2}{r}=\frac{d}{40}\]\[r=60 \text{ km}/h \]