What's the answer to this math problem? [63]

It's driving me nuts!!!

At the Indianapolis 500, Carter and Daniels were participants. Daniels' motor blew after 240 miles and Carter was out after 270 miles. If Carter's average rate was 20 mph more than Daniels' and their total time was 3 hours, how fast was each averaging?

Thanks in advance.

I've gotten the following on my own:

Distance of Carter + Distance of Daniel = 510 miles

Distance of Carter = 270 miles
Distance of Daniel = 240 miles

Rate of Carter = Rate of Daniel + 20 mph
Rate of Daniel = Rate of Daniel

Time of Carter + Time of Daniel = 3 hours
So... TC = 3 - TD and TD = 3 - TC

What am I missing? Or what have I done wrong?

Distance of Carter (Dc) = 270 miles
Distance of Daniel (Dd)= 240 miles
total time = 3 hours = (Dc/Vc) + (Dd/Vd) ....................(1)
Vc - Vd = 20mph...............................(2)
2 equations and 2 unknowns

Vc = Vd+20
replacing in (1)

3= 270/(Vd+20) +240/Vd => Vd = 160 mph (taking only positive) and hence Vc = 180 mph