Question

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?

Answer 1

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.