Question

Sarawong left the White House and drove toward his friend's house at an average speed of 60 km/h. Norachai left one hour later and drove in the same direction but with an average speed of 75 km/h. How long did Sarawong drive before Norachai caught up?

Answer 1

Sarawong drove for 5 hours before Norachai caught up, which was determined by setting up the equation based on the distance each person drove: 60 km/h × t = 75 km/h × (t - 1), and solving for t.

Step-by-step explanation:

To solve the problem of when Norachai caught up to Sarawong, we need to set up an equation that relates distance, speed, and time. Since distance is equal to speed multiplied by time (distance = speed × time), and both Sarawong and Norachai traveled the same distance, we can find out how long Sarawong drove before Norachai caught up.

Let's assign the variable t to represent the time (in hours) that Sarawong drove before Norachai caught up. Sarawong started an hour earlier, so Norachai drove for t - 1 hours when he caught up.

Now we'll use the formula for each person and set their distances equal to each other, because they will have covered the same distance at the point of catching up:

• Sarawong's distance: 60 km/h × t
• Norachai's distance: 75 km/h × (t - 1)

So we have the equation:

60t = 75(t - 1)

Expanding the right side we get:

60t = 75t - 75

Subtracting 75t from both sides, we get:

-15t = -75

Divide both sides by -15 to get the value of t:

t = 5

Therefore, Sarawong drove for 5 hours before Norachai caught up.