Bill drove from Ajax to Bixby at an average speed of 50 mph. On the way back he drove at 60 mph. The total trip took 42/5 hours of driving time. Find the distance between the two cities.
distance back= 60*42/5 miles
time on the way: distance/50=60*42/250
add the times.
To find the distance between the two cities, we need to use the formula distance = speed × time.
Let's assume that the distance between Ajax and Bixby is represented by the variable "d."
On the way to Bixby, Bill drove at an average speed of 50 mph. Let's denote the time it took him to travel that distance as "t1."
So, the distance from Ajax to Bixby can be calculated as d = 50 × t1.
On the way back, Bill drove at an average speed of 60 mph. The time it took him to travel the same distance (d) can be represented as "t2."
Therefore, the distance from Bixby to Ajax can be calculated as d = 60 × t2.
The total trip took 42/5 hours of driving time, which is the sum of the time it took Bill to drive to Bixby (t1) and back to Ajax (t2).
So, we have the equation t1 + t2 = 42/5.
Now, we can solve the system of equations to find the values of t1, t2, and ultimately the distance (d) between the two cities.
First, let's solve for t1:
t1 = (42/5 - t2)
Now, substitute this value of t1 in the equation for the distance from Ajax to Bixby:
d = 50 × (42/5 - t2)
Next, substitute the value of d from the equation for the distance from Bixby to Ajax:
d = 60 × t2
Now, equate the two expressions for d:
60 × t2 = 50 × (42/5 - t2)
Simplify the equation:
60t2 = 50(42/5 - t2)
Multiply through by 5 to eliminate the fraction:
300t2 = 210 - 50t2
Combine like terms:
350t2 = 210
Divide both sides by 350:
t2 = 210 / 350
Simplify:
t2 = 6/10
Therefore, t2 = 3/5.
Now, substitute this value of t2 back into the equation for d:
d = 60 × (3/5)
Simplify:
d = 36
Hence, the distance between the two cities, Ajax and Bixby, is 36 miles.