Pablo is driving 40 miles per hour. after he has driven 30 miles, his brother ricardo starts driving in the same direction. at what rate must ricardo drive to catch up with pablo in 5 hours?

, with explanation if you can

ANSWER:

The speed required by Ricardo to meet his brother after 5 hours is 46 miles per hour.    

SOLUTION:

Given, Pablo is driving 40 miles per hour and he has driven 30 miles already.

Now, his brother Ricardo started driving,  

We need to find the speed of Ricardo , so that he meets Pablo in 5 hours.  

When they meet after 5 hours, distance traveled by them will be equal so,

Distance traveled by Ricardo in 5 hours = 30 miles + distance covered by Pablo in 5 hours

Speed of Ricardo time taken = 30 + speed of Pablo time taken

Speed of Ricardo 5 = 30 + 40 × 5

Speed of Ricardo  5 = 30 + 200

Speed of Ricardo   5 = 230

Speed of Ricardo =

Speed of Ricardo = 46 miles per hour

Hence, the speed required by Ricardo to meet his brother after 5 hours is 46 miles per hour.

step-by-step explanation:

we have

using a graphing tool

see the attached figure

this is a quadratic equation (vertical parabola) open up

the vertex is a > vertex

the domain of the function is all real > interval (-∞,∞)

the range of the function is the > [-6.125,∞)

the function has two x->   and

the function is increasing over the > (0.25,∞)

the function is decreasing over the > (-∞,0.25)