Maths quiz anyone?

Question

Karen drives 210 miles in 4 hours. Her average speed is 60mph for part of the time and 40mph for the rest. For how long is her average speed 60 mph?

I NEED you to tell me how you worked it out using equations if you can- thank you very much if you can, this all helps towards my maths revision :)

Answer 1

let x = hours driven at 60mph
let y = hours driven at 40mph

60x + 40y = 210 miles
x + y = 4 hours

x=4-y substitute this equation into the first one

60(4-y) + 40y = 210
240 - 60y + 40y = 210
30 = 60y - 40y
30 = 20y
1.5 = y

x + y = 4
x + 1.5 = 4
x = 2.5
2.5 hours driving 60mph

Answer 2

Use a modified distance equation:

D(total) = v t + v ' t ', where v and t are her average speed and time for one part of the trip and v ' and t ' are the average speed and time for the other part of the trip.

If t + t ' = 4 hrs, then t ' = 4 - t and D(total) = 60 mph (t) + 40 mph (4 - t).

Now you can easily solve for t, the length of time she was traveling 60 mph.

Answer 3

60x + 40y = 210
4 (hours) = x + y
4 - x = y


60x + 40(4 - x) = 210
60x + 160 - 40x = 210
20x + 160 - 160 = 210 - 160
20x = 50
20x/20 = 50/20
x = 2.5

Therefore,
60(2.5) + 40(1.5) = 210

Karen drove 60mph for 2.5 hours and 40mph for 1.5 hours.

Answer 4

(1) 60x + 40y = 210
(2) x + y = 4

divide (1) by 40

(1) 1.5x+ y = 5.25
(2) x + y = 4

subtract (1) from (2)

0.5x = 1.25
x = 2.5

now find y by using x value 2.5

x + y = 4
2.5 + y = 4
y = 4 - 2.5
y = 1.5

Drive at 60mph for 2.5 hours, and 40mph for 1.5 hours

Answer 5

60x+40y=210
x+y=4

Just solve those two equations.