Algebra Question!

Question

Samuel left the house at noon heading to David’s store, 60 miles away. David left his store at 2 p.m., heading to Samuel’s house and traveling at twice Samuel’s speed. The two men met at 3 p.m. How fast was David traveling?

I got 24 miles per hour. Is this correct?

Answer 1

Relevant formula: d = t * r (distance = time * rate)

Total distance = 60 miles

Let ‘x’ represent the distance Samuel traveled, since the total distance between the two people is 60 miles, we know David must have then traveled (60 - x) miles.

David’s time: 3pm - 2pm = 1 hour

David’s rate: (60 - x) miles / hour = (60 - x) mi / hr

Samuel’s time: 3pm - 12pm = 3 hours

Samuel’s rate: x miles / 3 hours = x mi / 3 hr

Solving for x: (keep in mind David’s rate is twice as fast as Samuel’s rate)

(60 - x) = 2 (x / 3)

60 - x = 2x / 3

180 - 3x = 2x

180 = 5x

x = 36

‘x’ represents distance Samuel traveled

Recall that rate = distance / time,

David’s rate = (60 - 36) miles / 1 hour = 24 miles / hour

Meaning yes, you are correct that David traveled 60 - 36 = 24 miles in 1 hour or a rate of 24 miles per hour.