Hisako ran a crosscountry race in which the course was divid

Hisako ran a cross-country race in which the course was divided into 3 equal legs. Hisako ran the first leg at 12 km/h and the last two legs at 16 km/h. The whole race took her 50 min. How long was each leg? How long was the entire course?

I know the solution is something like this:
12t + 16t + 16t = d

Solution

seeing as the distances are all the same you have three legs whose additive times equal 50 min.
d=rt or:
t=d/r
d/12+d/16+d/16=5/6 find a common denominator for the left hand side of this equation.
48 looks like a good choice.
(4d+3d+3d)/48=5/6
10d/48=5/6 cross multiply
60d=5*48
60d=240
d=240/60
d=4 k for the distance of each leg.
proof
4/12+4/16+4/16=5/6
(4*4+3*4+3*4)/48=5/6
(16+12+12)/48=5/6
40/48=5/6
5/6=5/6