At 8 A.M., Dylan and his neighbor, Mickey, drove in their cars to a city that was 240 miles away from their neighborhood. When Dylan reached the city, Mickey had 40 miles to go. He finally completed the trip 48 minutes later. (a) How long did it take Mickey to drive to the city? (b) What was Dylan's driving speed in miles per hour? ( there were 3 similar problems posted on this website but none of them seemed to help me so I'm looking for someone that could thx :) )
an assumption is made that they each drive at some constant speed
Mickey ... 40 mi in 4/5 hr ... 40 / (4/5) = 50 mph
Dylan reached the city when Mickey had driven 200 mi ... in 4 hr at 50 mph
Dylan drove 240 mi in 4 hr ... speed = distance / time
yes it does
a. r = 40/(48/60) = 50 mi/h = Mickey's speed.
r * t = 240,
50t = 240,
t = 4.8 Hours = Mickey's speed.
b. 4.8 hours = Mickey's time.
4.8 - 48/60 = 4 Hrs. = Dylan's time.
r * t = 240,
r * 4 = 240,
r = Dylan's speed.
(a) Well, if Dylan traveled the entire 240 miles and Mickey had 40 miles left, we can deduce that Mickey traveled (240 - 40) miles = 200 miles. Since they both started at the same time, we can assume they traveled for the same duration. Therefore, it took Mickey the same amount of time to drive 200 miles as it took Dylan to drive 240 miles.
(b) Now, let's calculate Dylan's driving speed. We know the distance Dylan traveled (240 miles) and the time he took. However, we need to convert the time from minutes to hours. Since there are 60 minutes in an hour, 48 minutes is equivalent to 48/60 = 0.8 hours. So, Dylan's driving speed is 240 miles / 0.8 hours = 300 miles per hour.
Although, I must say, driving at 300 miles per hour would be quite impressive... and maybe just a tad illegal!
To solve this problem, we can break it down into two parts:
A) Finding the time it took Mickey to drive to the city
B) Finding Dylan's driving speed in miles per hour
Let's start with part A:
Since both Dylan and Mickey left their neighborhood at the same time, and Dylan reached the city when Mickey had 40 miles to go, we can assume that Dylan traveled the same distance as Mickey plus an additional 40 miles.
Let's represent the distance traveled by Mickey as 'd' miles.
So, Dylan traveled a total distance of (d + 40) miles, while Mickey traveled a distance of 'd' miles.
Now, we know that Dylan took 48 minutes longer to complete the trip than Mickey.
Since 1 hour is equal to 60 minutes, 48 minutes is equal to (48/60) hours, which is 0.8 hours.
Using the formula: speed = distance / time, we can calculate the time taken by Mickey to drive to the city.
Assuming Mickey's speed is 's' miles per hour, we have the equation:
d = s * t (Equation 1)
But we also know that Dylan traveled a total distance of (d + 40) miles at the same time Mickey traveled d miles.
So, we can write another equation:
(d + 40) = Dylan's Speed * (t + 0.8) (Equation 2)
Now, we have two equations with two variables: d (distance traveled by Mickey) and t (time taken by Mickey).
To solve these equations, we can use the substitution method.
First, we solve equation 1 for t:
t = d / s
Next, we substitute this value of t in equation 2:
(d + 40) = Dylan's Speed * (d / s + 0.8)
Now, we can solve this equation for d by simplifying:
(d + 40) = (d * Dylan's Speed / s) + (Dylan's Speed * 0.8)
Rearranging the terms, we get:
0.8 * Dylan's Speed = (40 * s) / (s - Dylan's Speed)
Simplifying further, we have:
0.8 * Dylan's Speed * (s - Dylan's Speed) = 40 * s
Expanding the terms, we get:
0.8 * s * Dylan's Speed - 0.8 * Dylan's Speed^2 = 40 * s
Rearranging the terms, we get the quadratic equation:
0.8 * Dylan's Speed^2 - 0.8 * s * Dylan's Speed + 40 * s = 0
Now, we can solve the above equation to find the value of Dylan's Speed, which is part B of the problem.
You can use the quadratic formula to solve the equation:
Dylan's Speed = (-b ± √(b^2 - 4ac)) / (2a),
where a = 0.8, b = -0.8s, and c = 40s.
Once you have the value of Dylan's Speed, you can substitute it back into equation 1 to find the value of 't', which will give you the answer to part A of the problem.