Time-Distance-Rate Question?

Question

To get to work Sam jogs 3 km to the train, then rides the remaining 5 km. If the train goes 40 km per hour faster than Sam's constant rate of jogging and the entire trip takes 30 min, how fast does Sam jog?

tried this problem, in the end my quadratic formula didn't factor so I did something wrong and can't find my mistake. I would really looovee step by step work to learn how to do this correctly. thanks!! :)

Answer 1

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Answer 2

Our basic equation is time = distance/rate.

Let r = Sam's jogging rate.

Let t1 = time to get to the train.

Then t1 = 3/r

The train's rate will be r + 40 and the distance is 5 km, so the time on the train (t2) is

t2 = 5/(r + 40)

We know that t1 + t2 = 30 min = 1/2 hour, so

3/r + 5/(r + 40) = 0.5

The common denominator is r(r + 40), so the left side becomes

[3(r + 40) + 5r]/r(r + 40) = 0.5

Multiply both sides by r(r + 40) to get

3(r + 40) + 5r = 0.5r(r + 40)

3r + 120 + 5r = 0.5r^2 + 20r

Combining terms gives

0.5r^2 + 12r - 120 = 0

Multiply by 2 to clear the fraction

r^2 + 24r - 240 = 0

The quadratic doesn't factor, so use the quadratic formula to get

r = (-24 + sqrt(1536))/2 = 7.5959 km per hour.

I apologize for not showing all the steps in the quadratic formula.