2. Rachael runs 2 km to her bus stop, and then rides 4.5 km to school. On average, the bus is 45 km/h faster than
Rachael’s average running speed. If the entire trip takes 25 min, how fast does Rachael run? (4 marks)
To solve this problem, we can use the formula:
Time = Distance / Speed
Let's break down the information given:
1. Rachael runs 2 km to her bus stop.
2. Rachael then rides 4.5 km to school.
3. The entire trip takes 25 minutes.
4. The bus is 45 km/h faster than Rachael's running speed.
Now, let's calculate the time it takes Rachael to run and ride the bus.
1. Time taken to run:
Distance = 2 km
Let's assume Rachael's running speed as R km/h.
Time taken to run = 2 / R
2. Time taken to ride the bus:
Distance = 4.5 km
Bus speed = R + 45 km/h (since the bus is 45 km/h faster than Rachael's speed)
Time taken to ride the bus = 4.5 / (R + 45)
3. The total time taken for the entire trip is 25 minutes, which can be converted to hours by dividing by 60:
Total time = 25 min / 60 = 25/60 hours = 5/12 hours
Now, we can set up the equation using the time formula:
Time taken to run + Time taken to ride the bus = Total time
2/R + 4.5/(R + 45) = 5/12
To solve this equation, we can cross multiply and simplify:
12(2/R) + 12(4.5/(R + 45)) = 5
24 + 54/(R + 45) = 5
54/(R + 45) = 5 - 24
54/(R + 45) = -19
Cross multiplying again:
54 = -19(R + 45)
Dividing by -19:
-54/19 = R + 45
Now, subtracting 45 from both sides:
-54/19 - 45 = R
Simplifying:
R = -54/19 - (45 * 19)/19
R = -1026/19
Therefore, Rachael's running speed is -1026/19 km/h.