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Alex777 [14]
4 years ago
15

Solve the problem by making up an equation. A man could arrive on time for an appointment if he drove the car at 40 mph; however

, since he left the house 15 minutes late, he drove the car at 50 mph and arrive 3 minutes early for the appointment. How far from his house was his appointment?
Mathematics
1 answer:
GenaCL600 [577]4 years ago
5 0

Answer: 60 miles


Step-by-step explanation:

Let x denote the distance between his home and the place of appointment and t be the time taken by him at 40 mph.

Also, Distance= Speed\times time

\\\Rightarrow\ x=40t.........................(1)

Since he left the house 15 minutes late, he drove the car at 50 mph and arrive 3 minutes early for the appointment.

15 minutes=\frac{15}{60}\ hour=0.25\ hour

3 minutes=\frac{3}{60}\ hour=0.05\ hour

Then actual time taken by him =t-0.25-0.05=t-0.30

\\\Rightarrow\ x=50(t-0.30)\\\Rightarrow\ x=50t-15.........................(2)

From (1) and (2), we have

40t=50t-15\\\Rightarrow\ 10t=15\\\Rightarrow\ t=\frac{3}{2}\ hour

Put the value of t in (1), we get

x=40\times\frac{3}{2}=60\ miles.........................(1)

Hence, the distance between his home and the place of appointment = 60 miles.


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