Speed equation.?

Question

Mary drove 400 KM in one hour less than John. If Mary's speed is 20 km/h faster than John's, what is an equation that can be used to determine J, john's speed?

Answer 1

Total distance (400 km)
M = Mary's speed
J = John's speed

Using distance = rate * time, for John:
John's time = 400/J

Using distance = rate * time, for Mary:
Mary's time = 400/M

M = J+20 (Mary speed is 20 more than John's)
Mary's time = 400/(J+20)
John's time = Mary's time + 1
John's time = 400/(J+20) + 1

So equating the two equations for John's time:
400/J = 400/(J+20) + 1

Multiply by (J+20)
(J+20)(400/J) = 400 + (J+20)
400 + 8000/J = 400 + J + 20

Subtract 400 from both sides:
8000/J = J+20

Multiply both sides by J:
8000 = J² + 20J

Subtract 8000 from both sides:
J² + 20J - 8000 = 0

Factoring:
(J + 100)(J - 80) = 0

J = 80 or -100 (and since John speed can't be negative, the only real answer is 80).

Checking our answer:
John was traveling 80 km/h
Mary was traveling 100 km/h
John took 5 hours (400/80)
Mary took 4 hours (400/100)

So, the equation is:
J² + 20J - 8000 = 0

Which can be factored as:
(J + 100)(J - 80) = 0

And solved as:
J = -100 or 80 (but we assume speed is positive...)

Thus, John was traveling 80 km/h

Answer 2

Let M be Mary's speed and J be John's speed. The first sentence can be phrased as
[1] ... 400 / M = (400 / J) - 1
and the second as
[2] ... M = 20 + J
Formula 1 without fractions is
[3] ... 400 J = (400 - J) M
Substituting formula 2 this becomes
[4] ... 400 J = (400 - J) (20 + J)
Work out the product
[5] ... 400 J = 8000 + 380 J - J^2
Simplifies to quadratic equation
[6] ... J^2 + 20 J - 8000 = 0
Solutions are J = -100 (nonsense) or J = 80

So John traveled 80 km/h, it took him 5 hours to drive 400 miles. Mary traveled 100 km/h and needed 4 hours.

Answer 3

John's speed = j km/hr
Mary's speed = (j + 20) km/hr

Mary's time = m hr
John's time = (m + 1) hr

400 = m(j + 20) = j(m + 1)
400 = mj + 20m = jm + j

j = 20m; substitute

400 = 20m^2 + 20m
0 = m^2 + m - 20
0 = (m + 5)(m - 4)
m = 4 (-5 not a possible solution to problem)

It took Mary 4 hours to travel 400 km. Her speed, therefore, was 100 km/hr. John, who took 5 hours, traveled at 80 km/hr.

Answer 4

M = Mary's speed
J = John's speed

M = J + 20

(400 / M) = Mary's time
(400 / J) = John's time

(400 / M) = (400 / J) + 1

Answer 5

400-20

Answer 6

400km/20km/h = Mary's Time
John's time = 1 h + Mary's Time
400km/John's Time = John's Velocity

Answer 7

You learn more if you do your own homework boss.