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.

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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

step-by-step explanation:

Answer from: Quest

2500

step-by-step explanation: