Question

Raphael is traveling in a straight line at a constant speed from point A to point B. His distance from point B in miles is-20t+ 45, where tis number of hours he has been traveling. What is his speed in miles per hour?

Answer 1

Speed = 20 mi/h

Step-by-step explanation:

There are two points A and B

Distance between both the points are define with function -20t + 45 miles

where t represent the number of hours of travelling.

Now firstly we find the initial position. At starting time is 0, so we put t=0 in given function of t.

At t=0;

d₀ = -20(0) + 45 = 0 + 45 = 45 miles

Now we find the distance travell after starting first hour.

Than we put t = 1 in the given function

At t = 1;

d₁ = -20(1) + 45 = -20 + 45 = 25 miles

Difference between d₁ & d₀ is

45 - 25 = 20 miles

We see that in one hour, total distace is covered 20 miles

Now we use time, speed, distance relation

Speed =
`(distance)/(time)`

S =
`(20)/(1)`

S = 20 miles/hour

That's the final answer.

I hope it will help you.