Is this math problem even solvable?

Question

I can't figure this out. The denominator of the function sort of makes sense as maybe the speed may not be more than 75mph for legal reasons, but here it goes:

Numerical and Graphical Analysis
A driver averaged 50 miles per hour on the round trip between Baltimore, Maryland and Philadelphia, Pennsylvania, 100 miles away. The average speeds for going and returning were x and y miles per hour, respectively.

(a) Show that y = 25x/(x-25)

(b) and (c) are easy to do, it was just a that no one I know has been able to answer correctly. I came up with a formula that was y = 100-x, which is different from this.

Jerry · Accepted Answer

The average speed is the total distance driven divided by the total time.  So let t be the total time driven and tx and ty be the time driven at x speed and ty at y speed, then:

t=total distance/total time
t=(100+100)/(50 miles/hr) = 4 hours

then to determine the average speed y and x:

y = 100/ty
x = 100/tx

We know that ty is the time left after driving tx

ty=t-tx

then replacing ty

y = 100/(t-tx)

y=100/(4-tx)

replacing tx with tx=100 miles / x speed or 100/x

y=100/(4-100/x)

and reducing

y=100x/(4x-100)

y=25x/(x-25)

quar_k8778 · Answer

The problem is meaningless, in a way. The average speeds to and from Philadelphia are the same, so y = x. 
To show this, substitute 50 for x and solve:  y = 25(50)/(50 - 25) = 25(50)/25 = 50

? · Answer

Average speed is 50 so the total driving time was 200/50 = 4 hours
100/x = driving time going
100/y = driving time returning

Sum of driving times:
 100/x + 100/y = 4

Divide by 4:
 25/x + 25/y = 1

Multiply by xy:
 25y + 25x = xy

Solve for y:
25y - xy = -25x
y(25-x) = - 25x
y(x-25) = 25x
y = 25x/(x-25)
...

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Is this math problem even solvable?

3 Answers