Question

Gabriella left Ted's house and drove south at an average speed of 26 km/h. Daniel left three hours later and drove in the same direction but with an average speed of 65 km/h. How long did Gabriella drive before Daniel caught up?

A) 2 hours
B) 3 hours
C) 4 hours
D) 5 hours

Answer 1

Gabriella drove for 2 hours before Daniel caught up. Daniel left 3 hours after Gabriella, and by equating their distances covered, we can find the time it took Daniel to catch up to Gabriella.

Step-by-step explanation:

To solve the problem concerning Gabriella and Daniel, we must determine how long Gabriella drove before Daniel caught up, given that Gabriella left first driving at 26 km/h, and Daniel left three hours later driving at 65 km/h.

Let t represent the time in hours that Gabriella drove before Daniel caught up. Since Gabriella had a three-hour head start, she drove for t + 3 hours by the time Daniel caught up.

The distance Gabriella covered is 26 km/h × (t + 3) hours, and the distance Daniel covered is 65 km/h × t hours. Both distances are equal when Daniel catches up:

• 26 km/h × (t + 3) = 65 km/h × t

Solving this equation gives us:

• 26t + 78 = 65t
• 78 = 39t
• t = 78 / 39
• t = 2 hours

So, Gabriella drove for 2 hours before Daniel caught up.

The answer is A) 2 hours.