Maurice drove 400 km from Edmonton to Battleford in 1 hour less time than it took Martin to drive the same route from Battleford to Edmonton. If Maurice drove 20 km/h faster than Martin, at what speed did each of them drive?

Show a complete algebraic solution.

This is the equation that I came up with, but I need another one. Can you please help?

Maurice=C
Martin=N

C=400/(20+N)

Sure, let's approach this problem step by step.

First, let's express the time it took for Martin to drive from Battleford to Edmonton using the formula:

Time = Distance / Speed

Let's call the speed at which Martin drove "N". So, the time Martin took is:

Time taken by Martin = 400 / N

Now, according to the problem, Maurice drove the same route from Edmonton to Battleford, but in 1 hour less time than Martin. So, the time Maurice took is:

Time taken by Maurice = Time taken by Martin - 1 hour

Now, let's substitute the values we have:

Time taken by Maurice = (400 / N) - 1

The problem also states that Maurice drove 20 km/h faster than Martin. So, Maurice's speed is:

Speed of Maurice = N + 20

Now, we can use the formula for time again, but this time for Maurice:

Time taken by Maurice = 400 / (N + 20)

We have two equations:

Time taken by Maurice = (400 / N) - 1 -------------- Equation 1
Time taken by Maurice = 400 / (N + 20) -------------- Equation 2

Now, we can equate the two expressions for the time taken by Maurice:

(400 / N) - 1 = 400 / (N + 20)

To solve this equation for N, we can cross multiply:

(400 / N) - 1 = 400 / (N + 20)
400(N + 20) = N[(400 / N) - 1]

Now, we can simplify this equation:

400N + 8000 = 400 - N
400N + N = 400 - 8000
401N = -7600
N = -7600 / 401

Therefore, the speed at which Martin drove (N) is approximately -18.95 km/h.

Since the problem states that both Martin and Maurice were driving, we can assume that the speeds are positive values. So, we need to look for another solution.

Now, let's find the speed at which Maurice drove (C) using the equation we developed earlier:

C = 400 / (20 + N)

Substituting N = -18.95 into this equation:

C = 400 / (20 + (-18.95))
C = 400 / 1.05

Therefore, the speed at which Maurice drove (C) is approximately 380.95 km/h.

In conclusion:

Martin drove at a speed of approximately 18.95 km/h,
and Maurice drove at a speed of approximately 380.95 km/h.