Question

A 10K run is 10 kilometers long. If 1 meter = 1.094 yards, use dimensional analysis to find the length of the race in miles. (Hint: 1 mile = 1760 yards). Round to the nearest tenth.

Answer 1

10936.1 yards = 10 kilometers 1 kilometer = 1093.1 yards

Answer 2

6.215 miles.

Explanation:

Given : A 10K run is 10 kilometers long.

To Find : find the length of the race in miles.

Solution:

Length of race = 10 km

1 k m = 1000 m

10 km = 10000 m

So, length of race in meters = 10000

Now 1 m = 1.094 yards

So, 10000 m =
`1.094 * 10000=10940` yards

Now 1760 yards = 1 mile

So, 1 yard =
`(1)/(1760) miles`

So, 10940 yards =
`(1)/(1760)  * 10940 miles`

So, 10940 yards =
`6.215 miles`

Hence the length of the race in miles is 6.215 miles.