The time t required to drive a certain distance varies inversely with the speed r. If it takes 4 hours to drive the distance at 35 miles per hour, how long will it take to drive the same distance at 45 miles per hour?

Question

A. about 3.11 hours
B. 140 hours
C. about 5.14 hours
D. 393.75 hours

Answer 1

The time t required to drive a certain distance varies inversely with the speed r. If it takes 4 hours to drive the distance at 35 miles per hour, how long will it take to drive the same distance at 45 miles per hour?

A. about 3.11 hours
B. 140 hours
C. about 5.14 hours
D. 393.75 hours

Answer 2

Using the inverse variation formula:

t = k/r

where t is the time, r is the speed, and k is a constant of proportionality.

To find k, plug in the given values:

4 = k/35

Solve for k:

k = 140

Now we can use k to find the time required at 45 miles per hour:

t = 140/45

t ≈ 3.11 hours

Therefore, the answer is A. about 3.11 hours.

Answer 3

or, in very simple steps:
distance driven = (4hrs)(35) mph = 140 km
time taken at 45 mph = 140 km/45 kmh = 3 1/9 hrs or 3.111.. hrs

Answer 4

Yes, that works too! Your method uses a more straightforward approach by finding the distance first and then dividing by the speed.