Question 65498
Abigail Nightwind has planned a bike trip with some friends from her village. They will bike for 8 hours, then hike for 4 hours. If they can bike on the average 10mph faster than they can hike and if they will cover a total of 122 miles, how fast can Abigail and her friends bike?
The formula for distance is: {{{highlight(d=rt)}}}, where d=distance, r=rate(or speed), and t=time
Givens for the hike protion:
t=4
r=r (we don't know it)
d=4r
Givens for the bike protion:
t=8
r=r+10 (10 mph faster than they can hike.)
d=8(r+10)
The total of the trip= 122
Problem to solve:
4r+8(r+10)=122
4r+8r+80=122
12r+80=122
12r+80-80=122-80
12r=42
12r/12=42/12
r=3.5
Therefore the rate that they can bike: r+10=3.5+10=13.5 mph
:
Sanity check:
If they hiked for 4 hrs at 3.5 mph and biked for 8 hrs at 13.5 mph, would they travel 122 mi?
4(3.5)+8(13.5)=122 ?
14+108=122
122=122  It appears we are sane.
Happy Calculating!!!!