Question 163973
Mary needs to go to Jane’s house. Mary drives 4 mph going uphill, goes 6 mph
on flat ground and goes 12 mph downhill. It takes her 1 hour to do the trip.
 How far is Jane’s house?
:
Let d = distance to house
;
Divide the distance into 4 + 6 + 12 = 22 units
:
The distance at each speed:
{{{4/22}}} = .182d; distance at 4 mph
{{{6/22}}} = .273d; distance at 6 mph
{{{12/22}}} = .545d; distance at 12 mph
:
Write a time equation, Time = dist/speed
{{{(.182d)/4}}} + {{{(.273d)/6}}} + {{{(.545d)/12}}} = 1
Clear the denominator multiply equation 12
3(.182d) + 2(.273d) + .545d = 12
:
.546d + .546d + .545d = 12
;
1.64d = 12
d = {{{12/1.64}}}
d = 7.3 miles
:
Interesting that this is the same distance if you just averaged the 3 speeds
{{{22/3}}} = 7.33 mi; in 1 hr, the distance would 7.33 mi