Question

The first part of a trip driving at 40 mph was 15 miles longer and took 30 minutes longer than the second part of the trip driving at 50 mph. What I'd the distance traveled?

Answer 1

Answer:

65 miles

Step-by-step explanation:

There are two simultaneous equations . Remeber that v=d/t, 1hour = 60 minutes.

1. 40 = (d+15)/(t+0.5)

2. 50 = d/t

solving: d= 25 miles and t=0.5 hours.

The distance traveled is:

D=d+d+15

D=65 miles

Answer 2

Answer:

$x = 65\,mi$

Step-by-step explanation:

Let assume that both trip occured at constant speed. Then, the definition of speed as the ratio of travelled distance to time is used in terms of the statement:

First trip:

$\frac{x + 15\,mi}{t+0.5\,h} = 40\,\frac{mi}{h}$

Second trip:

$\frac{x}{t} = 50\,\frac{mi}{h}$

After some algebraic handling, the following linear system is created:

$x - 40\cdot t = 5\\x - 50\cdot t = 0$

The solution of the linear system is:

$t = 0.5\,h, x = 25\,mi$

The distance travelled in both trips is:

$x = 65\,mi$