Question

Erik took a trip to see his friend Mike who lives 308 miles away. He left his place at 10 AM driving at 70 mph. In 2 hours, his friend Mike left his place driving towards Erik at an average speed of 50 mph. At what time will they meet?

Answer 1

Answer:

They will meet each other at 01 : 24 PM

Step-by-step explanation:

Distance = Speed × Time

When two person travel towards each other and start at the same time, then the distance between them is the sum of the distance each one will travel.

∵ Erik took a trip to see his friend Mike who lives 308 miles away

∴ The distance between Eric and Mike = 308 miles

∵ Eric left his place at 10 AM driving at 70 mph

∴ Eric's speed = 70 miles/hour

After two hours Mike left his place driving towards Erik

Assume that Eric's time is t hours

∵ Eric's time = t hours

∵ Mike started after Eric by two hours

∴ Mike's time = t - 2

∵ Mike drove at an average speed of 50 mph

∴ Mike's speed = 50 miles/hour

∵ Eric's distance + Mike's distance = 308

∵ Distance = Speed × Time

∴ Eric's distance = 70 × t = 70 t miles

∴ Mike's distance = 50 × (t - 2) = 50(t) - 50(2) = 50 t - 100 miles

∴ 70 t + 50 t - 100 = 308

- Add the like terms in the left hand side

∴ 120 t - 100 = 308

- Add 100 to both sides

∴ 120 t = 408

- Divide both sides by 120

∴ t = 3.4 hours

∵ 1 hour = 60 minutes

∴ 0.4 × 60 = 24 minutes

∴ t = 3 hours and 24 minutes

∴ They meet each other after 3 hours and 24 minutes from

   Eric started time

∵ Eric started at 10 AM

- Add 3 hours after 10 ⇒ 11 AM , 12 AM , 01 PM, then add 24 minutes

∴ They will meet each other at 01 : 24 PM