A motorist took a total of 4hr to drive from town A to town C. He took 1hr to travel from town A to town B,which is between town A & town C. The distance between town B & town C is 11/15 of the distance between town A and town C. If the total distance travelled is 360km,find the motorist's speed for the journey from town B to town C
AC = 360km.
BC = (11/15)360 = 264 km.
Speed=d/t = 264km / (4-1)hr = 88 mi/hr.
To find the motorist's speed for the journey from town B to town C, we need to first determine the distances traveled from town A to town B and from town B to town C.
Given that the motorist took a total of 4 hours to drive from town A to town C and 1 hour to travel from town A to town B, we can conclude that the motorist spent 4 - 1 = 3 hours traveling from town B to town C.
Let's assign variables to the distances traveled. Let x be the distance from town A to town B and y be the distance from town B to town C.
We know that the total distance traveled is 360 km. Substituting the given information, we have:
x + y + x = 360
2x + y = 360 ... (equation 1)
We are also given that the distance between town B and town C is 11/15 of the distance between town A and town C. This can be expressed as:
y = (11/15)(x + y)
Expanding and rearranging the equation, we have:
15y = 11x + 11y
4y = 11x
y = (11/4)x ... (equation 2)
Now, we can solve equations 1 and 2 simultaneously to find the values of x and y.
Substituting equation 2 into equation 1, we have:
2x + (11/4)x = 360
(8/4)x + (11/4)x = 360
(19/4)x = 360
19x = 1440
x = 1440/19
Now that we have the value of x, we can substitute it back into equation 2 to find y:
y = (11/4)(1440/19)
y = 440/19
Therefore, the distance from town B to town C is 440/19 km.
To find the motorist's speed for the journey from town B to town C, we divide the distance (440/19 km) by the time taken (3 hours):
Speed = Distance / Time
Speed = (440/19) / 3
Speed = 440 / (19 * 3)
Evaluating the expression, we get:
Speed ≈ 7.73 km/h
Therefore, the motorist's speed for the journey from town B to town C is approximately 7.73 km/h.