Question

A biker travels the 120 mi from New York , NY to Wilmington, DE in 8 hours. A bus, a truck, and a rider on a horse take the same route as the biker. At what speed does each of them travel if it takes them 2 hours, 2.5 hours, and 18.75 hours respectively to reach Wilmington? Do the speed and the time vary directly or inversely proportional when the same distance is traveled? Explain why.

Answer 1

Answer:

The speed is inversely proportional to the time when the same distance is traveled.

Step-by-step explanation:

Given that:

The distance traveled by the biker in 8 hours is 120 mi.

The speed of the biker=120/8=15 mi/hr.

[as speed=Distance travelled/Time taken]

As all take the same route, so the distance traveled by all is the same which is 120 mi

The time taken by the bus to cover this distance is 2 hours.

So, the speed of the bus = 120/2=60 mi/hr.

The time taken by the truck is 2.5 hours.

So, the speed of the truck = 120/2.5=48 mi/hr.

And the time taken by the rider is 18.75 hours.

So, the speed of the rider = 120/18.75=6.40 mi/hr.

Now, observe that to cover the same distance, the bus takes the least time, so, the bus is traveling at the fastest speed among all, while the rider has the slowest speed as the distance is the same for all. The truck and the biker have speed in between the speed of the bus and the rider.

It can be concluded that when the time of the journey for the same distance is less than speed is more.

So, the speed is inversely proportional to the time when the same distance is traveled.

Or, $\text{Speed}\propto\frac{1}{Time}$