Mathematics, 01.07.2019 10:30 jayzeptor

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.

Answers: 1

Show answers

Answers

Answer from: kamarionnatillman13

The motorist's average rate in the morning trip was 50 mph and that for the afternoon trip was 25 mph.

Step-by-step explanation:

Let the motorist's average rate in the afternoon = x mph.

It is given that his average rate in the morning was twice his average rate in the afternoon.

Therefore, his average rate in the morning = 2x mph.

Let t be the time taken for the morning trip.

It is given that he spent 5 hours for driving.

So, the time taken by him for the afternoon trip = 5 - t.

Now, using the formumla, $speed=\frac{distance}{time}$ ,

the verbal model for the morning trip is:

$2x=\frac{150}{t}$

xt = 75

The verbal model for the afternoon trip is:

$x=\frac{50}{5-t}$

5x - xt = 50

Substituting xt = 75, we get,

5x - 75 = 50

5x = 125

x = 25

2x = 50

Hence, his average rate in the morning trip was 50 mph and that for the afternoon trip was 25 mph.

Answer from: gabrielgutierrez730

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 miles in the morning and 50 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 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 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,

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

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://.

2. Learn more about equation of circle .

3. Learn more about range and domain of the function

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Speed and Distance

Keywords:Train, twice, fast, downhill, uphill, can go, 2/3 feet, level ground, speed, time, distance, 120 miles per hour downhill, flat land, travel, 45 miles.

Answer from: Quest

answer: the answer is ann

Answer from: Quest

step-by-step explanation:

i used the pitagoras theoreme

Arectangular sheet of paper is folded diagonally from f to h . what is the length of side gh?<

Another question on Mathematics

Mathematics, 21.06.2019 17:30

Graph the equation. select integers for x

Answers: 1

Answer

Mathematics, 21.06.2019 20:00

The marked price of an article is 25% above its selling price and the cost price is 30% less than its marked price . find the discount percent and gain percent. only a brainlest can solve it i will mark you brainlest

Answers: 2

Answer

Mathematics, 21.06.2019 23:00

Delbert keeps track of total of the total number of points he earns on homework assignments, each of which is worth 60 points. at the end of the semester he has 810 points. write an equation for delbert’s average homework score a in terms of the number of assignments n.

Answers: 3

Answer

Mathematics, 21.06.2019 23:30

Which of the following exponential functions goes through the points (1, 6) and (2, 12)? f(x) = 3(2)x f(x) = 2(3)x f(x) = 3(2)−x f(x) = 2(3)−x

Answers: 1

Answer

You know the right answer?

On a trip, a motorist drove 150 miles in the morning and 50 miles in the afternoon. his average rate...

Questions