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After riding a bicycle at a steady speed for 40 miles, John had a flat tire and walked 5 miles to a repair shop. His cycling rate was 4 times faster than his walking rate. If the time spent cycling and walking was 5 hours, at what rate was the cyclist riding?

Respuesta :

Answer:

Cycling rate = 12 mph

Explanation:

After riding a bicycle at a steady speed for 40 miles, John had a flat tire and walked 5 miles to a repair shop.

Total distance covered = 40 + 5 = 45 miles

His cycling rate was 4 times faster than his walking rate.

Let the walking rate be w.

Cycling rate = 4w

If the time spent cycling and walking was 5 hours

That is

               [tex]\frac{40}{4w}+\frac{5}{w}=5\\\\40w+20w=20w^2\\\\20w^2=60w\\\\w=3mph[/tex]

Cycling rate = 4w = 4 x 3 = 12 mph

Cycling rate = 12 mph

fichoh

Using the speed - time relation, the riding rate of the cyclist ls 12 miles per hour.

Let :

  • walking speed = s
  • Cycling speed = 4s
  • Total distance = 40 + 5 = 45 miles
  • Total time spent = 5 hours

Recall :

  • Time taken = Distance / speed

  • Walking time = 5/s

  • Cycling time = 40/4s

Total time taken = cycling time + walking time

5 = 5/s + 40/4s

5 = (20 + 40) / 4s

Cross multiply

4s × 5 = 60

20s = 60

s = 60/20

s = 3

Therefore, cycling speed = 4(3) = 12 miles per hour.

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