Two mechanics worked on a car. the first mechanic worked for 5 hours, and the second mechanic worked for 15 hours. together they charged a total of $1450 . what was the rate charged per hour by each mechanic if the sum of the two rates was $160 per hour

The first mechanic = a
the second mechanic = b

the first mechanic works for 4 hours = 4 * a
the second mechanic works for 15 hours = 15 * b
total charged = t

t = 4a + 15b

sum of their rates:
a + b = 160
b = 160 - a

t = 4a + 15b
1450 = 4a + 15 * (160 - a)
1450 = 4a + 2400 - 15a

now let's make the formula easier.

15a - 4a = 2400 - 1450
11a = 950

a = 86.36
b = 160 - 86.36 = 73.64