Jon and Remy were in a car race. When Jon finished the race in 45min, Remy had only driven 2/3 of the distance. Remy's average speed for the race was 50m/min less than Jon's.
a) Find the distance of the race.
b) What was Remy's speed?
REMY
Speed = X m/min.
d = X * 45 m.
JON
Speed = (X-50) m/min.
2d/3 = (x-50)*45.
Multiply both sides by 3/2:
d = 67.5(X-50).
Substitute 45x for d:
45x = 67.5x - 3375.
45x - 67.5x = -3375.
-22.5x = - 3375.
b. X = -3375 / -22.5 = 150 m/min = 150m/60s = 2.5 m/s = Remy's speed.
a. d = 45x = 45min * 150m/min = 6750 m.
Thank you.
To find the distance of the race, we can set up an equation using the given information. Let's use variable "d" to represent the distance of the race.
a) Since Jon finished the race in 45 minutes, we know that Remy had only driven 2/3 of the distance in that time. Hence, Remy's time can be calculated as (2/3) * 45 minutes.
To find Remy's speed, we'll use the formula: speed = distance / time. So Remy's speed can be calculated as d / [(2/3) * 45 minutes].
Since we are also given that Remy's average speed for the race was 50m/min less than Jon's, we can write Jon's speed as (Remy's speed + 50).
Now we'll use the formula for Jon's speed as well: Jon's speed = d / (45 minutes).
From the above information, we can write the equation:
d / [(2/3) * 45 minutes] = (d / 45 minutes) + 50
To solve this equation and find the value of "d," let's simplify it:
Multiply both sides of the equation by [(2/3) * 45 minutes] to eliminate the denominator:
d = (d / 45 minutes + 50) * [(2/3) * 45 minutes]
Simplifying further:
d = (2/3 * d + 50 * 45)
Multiply (2/3 * d) and (50 * 45):
d = (2/3 * d) + 2250
Subtract (2/3 * d) from both sides:
(1/3 * d) = 2250
Multiply both sides by 3 to isolate "d":
d = 2250 * 3
Calculating:
d = 6750 meters
Therefore, the distance of the race is 6750 meters.
b) Now let's find Remy's speed. We know that Remy's speed is d / [(2/3) * 45 minutes]. Substituting the value of "d" we found earlier:
Remy's speed = 6750 meters / [(2/3) * 45 minutes]
Simplifying:
Remy's speed = 6750 meters / [30 minutes]
Calculating:
Remy's speed = 225 meters/minute
Therefore, Remy's speed is 225 meters/minute.