solving equations in English

Systems of equations can be easily solved through the matrix. But when English is used, the difficulty of the problem is compounded. I am stumped by this question, I cannot figure out how to solve this question. Please help.

Jack drives from her country home to the city, a distance of 380 km. He drives part of the way on back roads, at an average speed of 50 km/h, and part on highways, at an average speed of 100 km/h. The trip takes 5 hours. How far does he drive on each type of road?

Answer key: 260 km on highways, 120 km on back roads

Thanks.