Question

A car passes a landmark on a highway traveling at a constant rate of 45 kilometers per hour. One hour later, a second car passes the same landmark traveling in the same direction at 65 kilometers per hour. How much time after the second car passes the landmark will it overtake the first car?

Answer 1

Answer:

2 hours 15 mins

Step-by-step explanation:

We know,

the speed of car 1 = 45 kilometers per hour; and

the speed of car 2 = 65 kilometers per hour

Assuming the time for the 2nd car to catch the 1st one to be t, we can write the distance equation:

$65t=45t+45$

$65t-45t=45$

$20t=45$

$t=45/20$

$t=2.25$

2.25 hours = 2 hours + (0.25 * 60) min = 2 hours 15 mins

Therefore, it takes 2 hours 15 mins for the second car to overtake first car after it passes the landmark.

Answer 2

A car passes a landmark on a highway traveling at a constant rate of 45 kilometers per hour.

Let t be the time taken by second car

So t+1 is the time taken by first car

Distance = speed * time

Distance traveled by first car = 45 * (t+1)

second car passes the same landmark traveling in the same direction at 65 kilometers per hour

Distance traveled by second  car = 65 * (t)

When second car overtakes the first car then their distance are same

65 t = 45(t+1)

65t = 45t + 45

Subtract 45 t from both sides

20t = 45

Divide both sides by 20

so $t = \frac{45}{20}=\frac{9}{4}=2.25$

It took 2.25 hours for the second car to overtake first car