kareem took 5 hours to drive 470km from Sudbury to Brantford. for part of the trip he drove at 100km/h. for the rest of the trip he drove at 90km/h. how far did he drive at each speed

He drove 200 km at 100 km/h and 270 km at 90 km/h

Step-by-step explanation:

Distance = Speed * Time

Assume that Kareem drove at 100 km/h for x hour

∵ Kareem drove at 100 km/h for x hours

∴ He drove a distance = 100 * x

∴ He drove a distance = 100 x km

∵ He took 5 hours in whole trip

- Subtract x from 5 to find the time that he took in the rest

of the trip

∴ The time of the rest of the trip = 5 - x hours

∵ For the rest of the trip he drove at 90 km/h

∴ He drove a distance = 90 * (5 - x)

∴ He drove a distance = 450 - 90 x

∵ He drove 470 km in whole trip

- Add the two distance and equate the sum by 470

∴ 100 x + 450 - 90 x = 470

- Add the like terms in the left hand side

∴ 10 x + 450 = 470

- Subtract 450 from both sides

∴ 10 x = 20

- Divide both sides by 10

∴ x = 2

Substitute the value of x in each distance to find the distance of each part

∵ The distance of the first part = 100 x

∴ The distance of the first part = 100 (2)

∴ The distance of the first part = 200 km

∵ The distance of the second part = 450 - 90 x

∴ The distance of the second part = 450 - 90 (2) = 450 - 180

∴ The distance of the second part = 270 km

He drove 200 km at 100 km/h and 270 km at 90 km/h