PLEASE!!!!

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:

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, [tex]speed=\frac{distance}{time}[/tex],

the verbal model for the morning trip is:

[tex]2x=\frac{150}{t}[/tex]

xt = 75

The verbal model for the afternoon trip is:

[tex]x=\frac{50}{5-t}[/tex]

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.




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

Further explanation:

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

[tex]\boxed{{\text{Speed}} = \frac{{{\text{Distance}}}}{{{\text{Dime}}}}}[/tex]

Given:

A motorist drove 150 miles in the morning and 50 miles in the afternoon.

The time taken to travel is [tex]5{\text{ hours}}.[/tex]

Explanation:

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

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

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

The time taken to 150 miles in the morning can be calculated as follows,

[tex]\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}[/tex]

The time taken to 50 miles in the afternoon can be calculated as follows,

[tex]\begin{aligned}{\text{speed}} &= \frac{{{\text{distance}}}}{{{\text{time}}}}\\x&= \frac{{50}}{{{t_2}}}\\{t_2}&= \frac{{50}}{x}\\\end{aligned}[/tex]

The total time taken by the person is 5 hours.

[tex]\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}[/tex]

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

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

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

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

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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.

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