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How long does it take to ride a bicycle 100 miles at each of the following speeds: 5 mph, 10 mph, 15 mph, 20 mph, 25 mph? What is always true about the product speed x time?

How long does it take to ride a bicycle 100 miles at each of the following speeds-example-1
User Milan Gajera
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1 Answer

22 votes
22 votes

Answer:

  • 5 mph ⇒ 20 h
  • 10 mph ⇒ 10 h
  • 15 mph ⇒ 6 2/3 h
  • 20 mph ⇒ 5 h
  • 25 mph ⇒ 4 h

speed × time = 100 miles

Explanation:

The graph shows an inverse relation between speed and time. You want to know what is true about the product of speed and time.

Inversely proportional

Two quantities are inversely proportional when one is proportional to the inverse of the other. A constant of proportionality will be involved. The relation can be written ...

y = k(1/x)

where x and y are the quantities inversely related, and k is the constant of proportionality.

Application

In the present case, we have a graph of the relation ...

time = distance/speed

where the distance is 100 miles.

Comparing this to the above inverse proportion relation, we see that "distance" is the constant of proportionality (k):

time = (100 miles)/speed

The times at various speeds are ...

  • 5 mph ⇒ 20 h
  • 10 mph ⇒ 10 h
  • 15 mph ⇒ 6 2/3 h
  • 20 mph ⇒ 5 h
  • 25 mph ⇒ 4 h

Multiplying both sides of this equation by speed, we get ...

speed × time = speed × (100 miles)/speed

speed × time = 100 miles

The product of speed and time is always 100 miles in this scenario.

User Craigb
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