Math Problem Statement

Shawn's engineering club is taking a trip by bus to a robotics fair. The fair is 175 miles from Shawn's school. The bus driver plans to stop and refuel after 2 hours, then complete the trip. The bus driver plans to drive at an average speed of 50 miles per hour. How many hours will the second part of the trip take? Write your answer as a whole number or a decimal. hours

Solution

To solve this problem, we need to determine the time for the second part of the trip. We are given the following information:

  • The total distance to the fair is 175 miles.
  • The bus driver will drive at an average speed of 50 miles per hour.
  • The bus will stop after 2 hours for refueling.

Step 1: Calculate the distance covered in the first 2 hours

The bus's speed is 50 miles per hour, and it will drive for 2 hours before stopping. The distance covered in the first 2 hours is:

Distance=Speed×Time=50miles per hour×2hours=100miles\text{Distance} = \text{Speed} \times \text{Time} = 50 \, \text{miles per hour} \times 2 \, \text{hours} = 100 \, \text{miles}

Step 2: Determine the remaining distance

The total distance to the fair is 175 miles, and the bus has already traveled 100 miles. The remaining distance is:

Remaining distance=175miles100miles=75miles\text{Remaining distance} = 175 \, \text{miles} - 100 \, \text{miles} = 75 \, \text{miles}

Step 3: Calculate the time for the second part of the trip

For the second part of the trip, the bus will still be traveling at an average speed of 50 miles per hour. To find the time for the second part of the trip, we use the formula:

Time=DistanceSpeed=75miles50miles per hour=1.5hours\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{75 \, \text{miles}}{50 \, \text{miles per hour}} = 1.5 \, \text{hours}

So, the second part of the trip will take 1.5 hours.


Would you like more details or have any questions?

Related Questions:

  1. How far would the bus travel if it drove for 3 hours at 50 miles per hour?
  2. What would the time be if the bus driver increased the speed to 60 miles per hour?
  3. If the bus made two stops instead of one, how would that affect the total travel time?
  4. How long would it take to complete the entire trip without a stop?
  5. What would the travel time be if the bus could only travel at 40 miles per hour?

Tip:

When dealing with travel problems, always break the trip into manageable parts and use the formula: Distance=Speed×Time\text{Distance} = \text{Speed} \times \text{Time}.

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Math Problem Analysis

Mathematical Concepts

Distance
Speed
Time

Formulas

Distance = Speed × Time
Time = Distance ÷ Speed

Theorems

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Suitable Grade Level

Grades 6-8