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
Step-by-step 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.
