Question

Two cyclists, 80 miles apart, start riding toward each other at the same time. One cycles 3 times as fast as the other. If they meet 2 hours later, what is the speed (in mi/h) of the faster cyclist?

Answer 1

The speed of the faster cyclist will be 30 miles/hour.

Explanation

One cyclist is 3 times as fast as the other.

Lets assume that the speed of the slower cyclist is  $x$ miles/hour.

So, the speed of the faster cyclist will be:  $3x$ miles/hour.

They start riding toward each other at the same time and meet 2 hours later.

We know that,  $Distance= speed*time$

So, the distance traveled by slower cyclist in 2 hours $= (x*2)miles= 2x$ miles and the distance traveled by faster cyclist $=(3x*2) miles = 6x$ miles.

Given that, they were 80 miles apart at the starting. So, the equation will be.....

$2x+6x=80\\ \\ 8x=80\\ \\ x=10$

So, the speed of the faster cyclist will be: (3×10)= 30 miles/hour.

Answer 2

The speed of a faster cyclist is 30 miles/hour.

Linear system

It is a system of an equation in which the highest power of the variable is always 1. A one-dimension figure that has no width. It is a combination of infinite points side by side.

Speed

It is the ratio of distance to time. and given by

$\rm Speed = \dfrac{distance }{time}$

Given

Two cyclists, 80 miles apart, start riding toward each other at the same time.

One cycles 3 times as fast as the other.

To find

The speed of a faster cyclist.

How to get the speed of a faster cyclist?

Let, x be the speed, for other cyclists, it will be 3x

Then according to the relative speed, if the direction is opposite the speed gets addded.

Speed = x + 3x = 4x

Distance = 80 miles

Time = 2 hours

Then

$\begin{aligned} \rm Speed &= \rm \dfrac{distance }{time}\\\\4x &= \dfrac{80}{2}\\\\4x &= 40 \\\\x &= 10\\\\\end{aligned}$

Speed of the other cyclist will be

3x = 3 (10) = 30

Thus, The speed of a faster cyclist is 30 miles/hour.

More about the linear system link is given below.

https://brainly.com/question/20379472