Answer:
The rate of the bike is approximately 23.14 mph
The rate of the bus is approximately 62.14 mph
Step-by-step explanation:
The given parameters are;
The time Janette spends on her bike to get to bus station = Half an hour = 0.5 hours = 30 minutes
The time Janette spends on the bus on her way to work = Two-thirds of an hour = 2/3 hours
The speed of the bus = 39 mph + The speed with which Janet travels on her bike
The total distance from her home to her work = 40 miles
To answer the question, let the speed with which Janet travels on her bike in miles per hour = x = the rate of the bike
Therefore, we have;
The speed rate of the bus = 39 + x
Distance = Speed × Time
The distance Janet travels to the bus station = The speed with which Janet travels on her bike × The time Janette spends on her bike to get to bus station
The distance Janet travels to the bus station = x × 0.5 = 0.5·x
The distance travelled by the bus from the bus station to her work = The speed of the bus × The time Janette spends on the bus from the bus station to her place of work
∴The distance travelled by the bus from the bus station to her work = (39 + x) × 2/3 hours = 13 + 2/3·x
The total distance from her home to her work = 40 miles = The distance Janet travels to the bus station + The distance travelled by the bus from the bus station to her work
∴ The total distance from her home to her work = 40 miles = 0.5·x + 13 + 2/3·x
Which gives;
40 = 0.5·x + 13 + 2/3·x
40 = 7/6·x + 13
7/6·x = 40 - 13 = 27
7/6·x = 27
x = 27 × 6/7 ≈ 23.14 mph
The rate of the bike = x ≈ 23.14 mph
The rate of the bike ≈ 23.14 mph
The speed rate of the bus = 39 + x ≈ 39 + 23.14 ≈ 62.14 mph
The speed rate of the bus ≈ 62.14 mph.
