Question

At 10:00 a.M., Han and Tyler both started running toward each other from opposite ends of a 10-mile path along a river. Han runs at a pace of 12 minutes per mile. Tyler runs at a pace of 15 minutes per mile. How far does Han run after a half hour? After an hour? Do Han and Tyler meet on the path within 1 hour? Explain or show your reasoning.

Answer 1

How far does Han run after a half hour? 2.5 miles

After an hour? 5 miles

Do Han and Tyler meet on the path within 1 hour? No

Explanation:

Given Han runs at a pace of 12 minutes per mile, then in 30 minutes he run:

`30 minutes * (1 mile)/(12 minutes) = 2.5 miles`

and in an hour he run:

`60 minutes * (1 mile)/(12 minutes) = 5 miles`

Given Tyler runs at a pace of 15 minutes per mile, then in 60 minutes he run:

`60 minutes * (1 mile)/(15 minutes) = 4 miles`

Therefore, after one hour Han and Tyler run a combined distance of 5 + 4 = 9 miles which is less than the 10 miles of distance between them at the beginning, that means they will be at 1 mile of distance of each other.

Answer 2

Answer: 1. Han run 2.5 miles after a half hour.

2. No, they will not meet within 1 hour.

Explanation:

Here, Han runs at a pace of 12 minutes per mile.

Or, we can say that he can run with the speed of 5 miles per hour. (because, speed = 1/pace and 12 minutes = 1 miles ⇒ 60 minutes = 5 miles)

Similarly, If Tyler runs at a pace of 15 minutes per mile ⇒ Tyler run with the speed of 4 miles per hour.

Therefore,

1) The distance covered by Han in half an hour = 1/2 × 5 = 2.5 miles

(because distance = speed × time)

Now, 2) the time at which Han and tyler will meet,

T= Total distance/ ( the sum of their speed)

`T= (10)/(5+4) = (10)/(9)`

⇒
`T = 1(1)/(9)` hours > 1 hour

That is, they will not meet within 1 hour.