Thread: How do you slove this Speed Equation?

At 9:00 Saturday morning, two bicyclists are heading in opposite directions pass each other on a bicycle path. The bicycle heading north is zriding 5km/h faster than the bicyclist hading south. At 10:45 they are 40.25 km. apart. Find the two bicyclists rates.

Originally Posted by poohbearjkr

At 9:00 Saturday morning, two bicyclists are heading in opposite directions pass each other on a bicycle path. The bicycle heading north is zriding 5km/h faster than the bicyclist hading south. At 10:45 they are 40.25 km. apart. Find the two bicyclists rates.

Both are moving at a constant speed. Let's call the speed of the bike heading South v. Then the speed of the bike heading North is v + 5 km/h. We know they meet at 9 and are 40.25 km at 10:45 which is 1.75 hours later.

For constant speed v = d/t where d is the distance travelled and t is the time it takes to travel it. Let's say that the bike travelling South covered a distance of x km and the bike travelling North has covered y km. Then:
x + y = 40.25

From the speed equation for each biker:
v = x/1.75
v + 5 = y/1.75

We want to find v.

So take the first equation and solve it for y:
y = 40.25 - x
and put this into the third equation:
v + 5 = (40.25 - x)/1.75

Now solve the second equation for x:
x = 1.75*v
and put this into the last equation we just got:
v + 5 = (40.25 - [1.75*v])/1.75

This is one equation in one unknown, which you can solve. I got v = 9 km/h. If you need help solving the equation, just let me know.

-Dan