# Distance

• Feb 8th 2007, 06:29 PM
jarny
Distance
Some friends on a hike leave at 9a.m. and return at 2p.m. They spend one-quarter of the total distance walking uphill, one-half walking on level ground, and one-quarter walking downhill. If their speed is 4 mph on level ground, 2 mph uphill, and 6 mph downhill, approximately how far did they walk? I came to the answer of 20 miles. Is this correct? Thanks
• Feb 8th 2007, 08:24 PM
Soroban
Hello, jarny

Quote:

Some friends on a hike leave at 9 a.m. and return at 2 p.m.
They spent one-quarter of the total distance walking uphill at 2 mph,
one-half walking on level ground at 4 mph,
and one-quarter walking downhill at 6 mph.
How far did they walk?

Formula: .Distance .= .Speed x Time . ---> . T = D ÷ S

Let x = total distance.

They walked ¼x miles uphill at 2 mph. .This took: ¼x ÷ 2 = x/8 hours.

They walked ½x miles level at 4 mph. .This took: ½x ÷ 4 = x/8 hours.

They walked ¼x miles downhill at 6 mph. .This took: ¼x ÷ 6 = x/24 hours.

The total time was 5 hours: . x/8 + x/8 + x/24 .= .5

Multiply by 24: .3x + 3x + x .= .120 . ---> . 7x .= .120

Therefore, the distance is: . x .= .120/7 miles.