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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.