Find the speed...

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• Dec 18th 2007, 10:44 AM
free_to_fly
Find the speed...
Here's a problem that I cam across the other day, I can't seem to find the answer though at first glance the question looks relatively simple.

There is a 2mile stretch of road. I drive down the first mile with an average speed of 30mph, find what speed I must travel down the remaining mile for my overall average speed to be 60mph.

At first I thought time=distance/speed, so 2/(30+x)=2/60, but that yields the incorrect answer. Does it have something to do with the harmonic mean? Can someone help?
• Dec 18th 2007, 12:14 PM
colby2152
Quote:

Originally Posted by free_to_fly
Here's a problem that I cam across the other day, I can't seem to find the answer though at first glance the question looks relatively simple.

There is a 2mile stretch of road. I drive down the first mile with an average speed of 30mph, find what speed I must travel down the remaining mile for my overall average speed to be 60mph.

At first I thought time=distance/speed, so 2/(30+x)=2/60, but that yields the incorrect answer. Does it have something to do with the harmonic mean? Can someone help?

I was stumped!
• Dec 18th 2007, 12:34 PM
CaptainBlack
Quote:

Originally Posted by free_to_fly
Here's a problem that I cam across the other day, I can't seem to find the answer though at first glance the question looks relatively simple.

There is a 2mile stretch of road. I drive down the first mile with an average speed of 30mph, find what speed I must travel down the remaining mile for my overall average speed to be 60mph.

At first I thought time=distance/speed, so 2/(30+x)=2/60, but that yields the incorrect answer. Does it have something to do with the harmonic mean? Can someone help?

To drive 2 miles at an average speed of 60mph takes 1/30 of an hour.

You have already driven 1 mile at 30mph, which took 1/30 hour

So you must drive the final mile at $\infty$mph

RonL
• Dec 18th 2007, 06:45 PM
topsquark
Quote:

Originally Posted by free_to_fly
Here's a problem that I cam across the other day, I can't seem to find the answer though at first glance the question looks relatively simple.

There is a 2mile stretch of road. I drive down the first mile with an average speed of 30mph, find what speed I must travel down the remaining mile for my overall average speed to be 60mph.

At first I thought time=distance/speed, so 2/(30+x)=2/60, but that yields the incorrect answer. Does it have something to do with the harmonic mean? Can someone help?

This is a variation of a Mensa question. I love this one!

-Dan
• Dec 19th 2007, 05:37 AM
Soroban
Hello, free_to_fly!

As Dan pointed out, this is a classic problem . . .

Quote:

There is a 2-mile stretch of road.
I drive down the first mile with an average speed of 30 mph.
What speed must I travel on the remaining mile
for my overall average speed to be 60 mph?

To average 60 mph over the 2-mile road,
. . you must cover the distance in: . $\frac{\text{2 miles}}{\text{60 mph}} \:=\:\frac{1}{30}\text{ hours} \:=\:2\text{ minutes}$

You have already driven 1 mile at 30 mph.
. . This took you: . $\frac{\text{1 mile}}{\text{30 mph}}\:=\:\frac{1}{30}\text{ hours} \:=\:2\text{ minutes}$

You have already used up all of the allotted time.
. . It is impossible to drive the last mile in 0 minutes.