A man rode a bicycle for 12 miles and then hiked an additional 8 miles. The total time for the trip was 5 hours. If his rate when he was riding a bicycle was 10 miles per hour faster than his rate walking, what was each rate?​

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!

A man rode a bicycle for 12 miles and then hiked an additional 8 miles. The total time for the trip was 5 hours. If his rate when he was riding a bicycle was 10 miles per hour faster than his rate walking, what was each rate?

Walking DATA:

distance = 8 miles ; rate = x mph ; time = 8/x hrs.

Biking DATA:

distance = 12 miles : rate = (x+10)mph ; time = 12/(x+10) hrs

Equation:

8/x + 12/(x+10) = 5

Multiply thru by x(x+10) you get:

8(x+10) + 12x = 5x(x+10)

8x + 80 + 12x = 5x^2 + 50x

5x^2 + 30x - 80 = 0

x^2 + 6x - 16 = 0

(x+8)(x-2) = 0

---

Positive solution:

x = 2 mph (walking rate)

x+10 = 12 mph (bicycling rate)

Cheers,

Stan H.

126.66 m²

step-by-step explanation:

the pertinent area formula is a = πr², where r is the radius.

here, a = π(6.35 m)² = 40.32π, or approximately 126.66 m²