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.
Hello, shenton!
I use baby-talk with such word problems . . . it works for me.
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
There are a number of approaches to this problem.
If you prefer a system of equations, we can do it like this . . .
Let = number of km on back roads.
Let = number of km on highways.
. . We know that: . (1)
He drove km at 50 km/hr.
. . This took him hours.
He drove km at 100 km/hr.
. . This took him hours.
Since his total time was 5 hours, we have: .
. . Multiply by 100: . (2)
Solve the system of equations: .
Subtract (1) from (2): .
Substitute into (1): .
Therefore, Jack drove: .