Cecile took a ferry to corss the St.Laurent River rom Sept-Iles, PQ to Matane,PQ a distance of 175km. She relizes that it's the same road distance from her home to her cottage in Godbout, PQ. By road, she averages 60km/h faster than the ferry and takes 5 h 20 min less time. What's the speed of the ferry?
speed of ferry ---- x km/h
speed of car ----- x+60 km/h
time for ferry = 175/x
time by car = 175/(x+60)
What are you told about these times?
Form your equation from that fact.
To solve this problem, we can use the formula:
Time = Distance / Speed
Let's assume the speed of the ferry is x km/h.
According to the given information, Cecile takes 5 hours and 20 minutes less time to travel the same road distance (175 km) by car compared to the ferry. This can be converted to hours:
5 hours + (20 minutes / 60) = 5.33 hours
Using the formula, we can find the time taken by the ferry and the car separately.
Time taken by the ferry = Distance / Speed of the ferry
Time taken by the car = Distance / (Speed of the ferry + 60)
Now, let's calculate the time taken by the ferry:
Time taken by the ferry = 175 km / x km/h
Next, let's calculate the time taken by the car:
Time taken by the car = 175 km / (x + 60) km/h
According to the given information, the time taken by the car is 5.33 hours less than the time taken by the ferry:
Time taken by the car = Time taken by the ferry - 5.33
175 km / (x + 60) km/h = 175 km / x km/h - 5.33
To solve for x, we need to rearrange the equation:
175 km / (x + 60) km/h + 5.33 = 175 km / x km/h
Multiply both sides of the equation by x(x + 60) to eliminate the denominators:
175 km(x) + 5.33(x)(x + 60) = 175 km(x + 60)
175x + 5.33(x^2 + 60x) = 175x + 10500
175x + 5.33x^2 + 319.8x = 175x + 10500
Rearrange the equation:
5.33x^2 + 319.8x = 10500
Now we can solve this quadratic equation to find the value of x. You can use factoring, completing the square, or the quadratic formula to solve for x.
Once you find the value of x, that will be the speed of the ferry.