At 8 A.M., Dylan and his neighbor, Mickey, drove in their cars to a city that was 240 mi. away from their neighborhood. When Dylan reached the city, Mickey had 40 mi. 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 mph?

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To find the answer to these questions, we can use the formula: Speed = Distance / Time.

a) To find how long it took Mickey to drive to the city, we need to calculate his driving time. Let's denote Mickey's driving time as "t". Since we know the distance from the city when Dylan reached it was 40 miles, we can set up the equation:

40 miles = Mickey's driving speed * t

Now, we need to find Mickey's driving speed. We know that Dylan's driving time was the same as Mickey's driving time, plus an additional 48 minutes (0.8 hours) since he arrived at the destination earlier. Therefore, we can set up another equation:

240 miles = Dylan's driving speed * (t + 0.8)

We can rearrange the second equation to solve for Dylan's driving speed:

Dylan's driving speed = 240 miles / (t + 0.8)

Now, substitute the value of Dylan's driving speed into the first equation:

40 miles = (240 miles / (t + 0.8)) * t

Solve for t:

40(t + 0.8) = 240t

40t + 32 = 240t

200t = 32

t = 32 / 200

t = 0.16 hours

Therefore, it took Mickey 0.16 hours to drive to the city.

b) Now, let's calculate Dylan's driving speed using the equation:

Dylan's driving speed = 240 miles / (t + 0.8)

Dylan's driving speed = 240 miles / (0.16 + 0.8)

Dylan's driving speed = 240 miles / 0.96

Dylan's driving speed ≈ 250 miles per hour

Therefore, Dylan's driving speed was approximately 250 mph.

To answer these questions, we can use the information that Dylan and Mickey traveled a total distance of 240 miles from their neighborhood to the city. We also know that when Dylan reached the city, Mickey had 40 miles left to drive, and he completed the trip 48 minutes later.

a) To find out how long it took Mickey to drive to the city, we need to calculate the time it took for him to cover the remaining 40 miles. We know that the entire trip took Dylan and Mickey the same amount of time, so the time it took for Mickey to cover the remaining distance is equal to the time it took Dylan to cover the full distance.

Let's assume it took them t hours to complete the trip. Dylan drove the first 240 miles, so he covered 240 miles in t hours. Mickey, on the other hand, covered the remaining 40 miles in t hours plus an additional 48 minutes, which is equal to 48/60 = 0.8 hours.

Since the time it took Dylan to cover 240 miles is equal to the time it took Mickey to cover 40 miles plus 0.8 hours, we can set up the equation:

240 miles = 40 miles + 0.8 hours

Simplifying the equation, we have:

200 miles = 0.8 hours

To find the time it took Mickey to drive to the city, we divide both sides of the equation by the distance Mickey traveled:

t = 0.8 hours

Therefore, it took Mickey 0.8 hours (or 48 minutes) to drive to the city.

b) To find Dylan's driving speed in miles per hour (mph), we can use the formula:

Speed = Distance / Time

We know that Dylan's total distance was 240 miles, and it took him t hours to cover that distance. Therefore, his speed can be calculated as:

Dylan's speed = (240 miles) / (t hours)

Since t is the same for both Dylan and Mickey, we can use the value of t we calculated in part a) which is 0.8 hours:

Dylan's speed = 240 miles / 0.8 hours

Simplifying the equation:

Dylan's speed = 300 miles per hour

Therefore, Dylan's driving speed was 300 mph.