John leaves point A to travel 360klm and Joanne leaves point A 40 mins later and her cars speed is 18klm per hour faster than John's but they both arrive at the same time. What is their respective speeds?
The both travel the same distance.
distance=rate(time)
distanceJohn= rateJohn*timejohn
distanceJoanne=(rateJOhn+18)(timejohn-40/60)
both distances are the same, 360km.
First, let's calculate the distance John travels. We know that distance = rate * time.
Let's say John's speed is represented by r (in km/h). John's time is the same as Joanne's time, so we can represent it as t (in hours).
Therefore, the distance John travels can be written as:
distanceJohn = r * t
Now let's calculate the distance Joanne travels. We know that Joanne's car speed is 18 km/h faster than John's, so we can represent it as r + 18. Joanne's time is 40 minutes (or 40/60 = 2/3 hours) less than John's time, so we can represent it as t - 2/3.
Therefore, the distance Joanne travels can be written as:
distanceJoanne = (r + 18) * (t - 2/3)
Since both John and Joanne travel the same distance of 360 km, we can set up an equation:
distanceJohn = distanceJoanne
r * t = (r + 18) * (t - 2/3)
Now we can solve this equation to find the respective speeds of both John and Joanne.
Simplifying the equation:
rt = (r + 18) * (t - 2/3)
rt = rt + 18t - 2r - 12
0 = 18t - 2r - 12
2r = 18t - 12
Dividing both sides of the equation by 2:
r = 9t - 6
Now we can substitute this expression for r in the earlier equation:
distanceJohn = r * t
360 = (9t - 6) * t
360 = 9t^2 - 6t
9t^2 - 6t - 360 = 0
Using the quadratic formula: t = (-b ± √(b^2 - 4ac)) / (2a), where a = 9, b = -6, and c = -360.
t = (-(-6) ± √((-6)^2 - 4 * 9 * -360)) / (2 * 9)
t = (6 ± √(36 + 12960)) / 18
t = (6 ± √12996) / 18
Since time can't be negative, we can discard the negative solution.
t = (6 + √12996) / 18
Simplifying the expression under the square root:
t = (6 + √(4 * 3249)) / 18
t = (6 + √(4) * √(3249)) / 18
t = (6 + 2 * 57) / 18
t = (6 + 114) / 18
t = 120 / 18
t = 6.67 hours
Now we can substitute the value of t back into the expression for r:
r = 9t - 6
r = 9 * 6.67 - 6
r = 60.03 km/h
Therefore, John's speed is approximately 60.03 km/h.
Since Joanne's speed is 18 km/h faster than John's, her speed is:
Joanne's speed = John's speed + 18
= 60.03 + 18
= 78.03 km/h
Therefore, Joanne's speed is approximately 78.03 km/h.