word problem that stumped Einstein (at first)

[renegade05]

Distance, Time, and Speed.

An old car has to travel a 2-mile route, uphill and down. Because it is so old, the car can climb the first mile - the ascent - no faster than an average speed of 15mi/h. How fast does the car have to travel the second mile - on the descent it can go faster, of course - in order to achieve an average speed of 30 mi/h for the trip.

Apparently Einstein was given this problem by his friend Wertheimer. It stumped him at first but later realized the answer is, there is no time available for the downhill run.

I made an equation like this:

x = speed for downhill run

\(\displaystyle 30 mi/hour average speed = \frac{2-mile-route}{\frac{1 mile-ascent}{15mi/hour}+\frac{1 mile -descent}{x}}\)

Indeed, I cannot slove for X. Someone please explain this to me.... I can't wrap my head around it.

 

[lookagain]

I made an equation like this:

x = speed for downhill run

\(\displaystyle 30 mi/hour average speed = \frac{2-mile-route}{\frac{1 mile-ascent}{15mi/hour}+\frac{1 mile -descent}{x}}\)

Indeed, I cannot slove for X. Someone please explain this to me.... I can't wrap my head around it.

Muliply the "larger" fraction by \(\displaystyle \frac{15x}{15x}\)

\(\displaystyle 30 = \frac {2(15x)}{x + 15}\)

Cross-multiply:

\(\displaystyle 30(x + 15) = 30x\)

\(\displaystyle 30x + 450 = 30x\)

\(\displaystyle 450 = 0\)

False. No solution. Impossible.

It can't be done.