afreemanny said:
Two bikers leave the Harley-Davidson shop, traveling on the same road and in the same direction. One biker drives 5 mph faster than the other. The faster biker stops after 1 1/2 h but the slower biker stops after 1 h. If the two bikers are 32 1/2 miles apart, what was the speed of each biker?
** Warning ** This LOOKS W-A-A-A-A-Y more scary than it is. Just go one step at a time, slowly and easily. understand each step.
Make definitions for stuff you need.
B = Speed of Faster Biker
K = Speed of Slower Biker
Distance = Rate * Time <== I just wrote this because I thought I might need it.
"One biker drives 5 mph faster than the other."
B = K + 5 mph
Now we have a problem. Your problem statement did not state that they left at the same time. We'll have to assume that.
A little thinking is required. The faster biker drove for more time. Oh, then he must be way beyond the other.
Write the equations.
Distance<sub>1</sub> = Rate<sub>1</sub>*Time<sub>1</sub>
Distance<sub>2</sub> = Rate<sub>2</sub>*Time<sub>2</sub>
Sustitute what we know or have defined.
Distance<sub>1</sub> = B*Time<sub>1</sub>
Distance<sub>2</sub> = K*Time<sub>2</sub>
"The faster biker stops after 1 1/2 h but the slower biker stops after 1 h."
Time<sub>1</sub> = 1.5 hour
Time<sub>2</sub> = 1.0 hour
Distance<sub>1</sub> = B*1.5 hr
Distance<sub>2</sub> = K*1.0 hr
"the two bikers are 32 1/2 miles apart"
Distance<sub>1</sub> = Distance<sub>2</sub> + 32.5
Distance<sub>2</sub> + 32.5 mi = B*1.5 hr
Distance<sub>2</sub> = K*1.0 hr
B = K + 5 mph
Distance<sub>2</sub> + 32.5 mi = (K + 5 mph)*1.5 hr
Distance<sub>2</sub> = K*1.0 hr
Whew! That was a lot to keep track. Just one step at a time. Don't try to do too much at once.
Old addage - Solve for what you DON'T want. The problem statement wants the speeds.
Distance<sub>2</sub> = (K + 5 mph)*1.5 hr - 32.5 mi
Distance<sub>2</sub> = K*1.0 hr
Transitive Property of Equals.
(K + 5 mph)*1.5 hr - 32.5 mi = K*1.0 hr
Solve for 'K'
1.5*K*hr + 7.5*mi - 32.5*mi = K*hr
0.5*K*hr = 25 mi
K*hr = 50*mi
K = 50 mph <== If your units don't come out right, you did something wrong.
B = K + 5 mph = 55 mph
Great. Now, let's test it.
55 mph * 1.5 hr = 82.5 mi
55 mph * 1.0 hr = 50.0 mi
82.5 mi - 50.0 mi = 32.5 mi
Looks good.
