Question

On a trip, a motorist drove 150 miles in the morning and 50 miles in the afternoon. His average rate in the morning was twice his average rate in the afternoon. He spent 5 hours driving. Find his average rate on each part of the trip.

Answer 1

A motorist drove 150 miles in the morning and;

50 miles in the afternoon

His average rate in the morning was twice his average rate in the afternoon

He spent 5hrs driving

Let the times spent driving in the morning be x

Average speed = Distance ÷ time

$\frac{150}{x}$ = 2($\frac{50}{5 - x}$)

Cross multiplying gives;

750 - 150x = 100x

250x = 750 , x =3

Average speed in the morning is 150/3 = 50miles/hr

Average speed in the afternoon = 50/(5-3) = 25miles/hr

Answer 2

The average speed in the morning trip is $50{\text{ mile/h}}$ and the speed in the afternoon trip is $25{\text{ mile/h}}.$

Further explanation:

The relationship between speed, distance and time can be expressed as follows,

$\boxed{{\text{Speed}} = \frac{{{\text{Distance}}}}{{{\text{Dime}}}}}$

Given:

A motorist drove $150{\text{ miles}}$ in the morning and $50\:{\text{miles}}$ in the afternoon.

The time taken to travel is $5{\text{ hours}}.$

Explanation:

The average rate in the morning was twice his average rate in the afternoon.

Consider the speed of the person in afternoon be $x{\text{ miles/hour}}.$

So speed of the person in the morning is $2x{\text{ miles/hour}}.$

The time taken to $150\: {\text{miles}$ in the morning can be calculated as follows,

$\begin{aligned}{\text{speed}}&=\frac{{{\text{distance}}}}{{{\text{time}}}}\\2x&=\frac{{150}}{{{t_1}}}\\{t_1}&= \frac{{150}}{{2x}}\\{t_1}&=\frac{{75}}{x}\\\end{aligned}$

The time taken to $50\:{\text {miles}$ in the afternoon can be calculated as follows,

$\begin{aligned}{\text{speed}}&=\frac{{{\text{distance}}}}{{{\text{time}}}}\\x&= \frac{{50}}{{{t_2}}}\\{t_2}&=\frac{{50}}{x}\\\end{aligned}$

The total time taken by the person is 5 hours.

$\begin{aligned}t&= {t_1} + {t_2}\\5&=\frac{{75}}{x} + \frac{{50}}{x}\\5&= \frac{{75 + 50}}{x}\\x&= \frac{{125}}{5}\\x &= 25\\\end{aligned}$

The speed of the person in the afternoon is $25{\text{ miles/h}}.$

The speed of the person in the morning can be calculated as follows,

$\begin{aligned}{\text{Speed} &= 2\times 25\\&= 50{\text{ miles/h}}\\\end{aligned}$

The average speed in the morning trip is $\boxed{50{\text{ mile/h}}}$ and the speed in the afternoon trip is $\boxed{25{\text{ mile/h}}}.$

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Speed

Keywords: motorist, 150 miles, drove, morning, afternoon, twice, spent, trip, average rate, 5 hours driving, 50 miles.