John's family travels 300km from their home to a family reunion. His cousin Suzan and her family take the same amount of time to travel 200km from their home. Determine the speed of both vehicles given that one of the vehicles travels 30km/h faster than the other.
the faster vehicle travels 3/2 as fast as the slower vehicle.
So, if x is the slower vehicle's speed,
3/2 x = x+30
x = 60
check: 200/60 = 300/90
Let's assume the speed of John's family vehicle is x km/h.
According to the given information, we know that Suzan's family vehicle travels 30 km/h slower, so the speed of Suzan's family vehicle is (x-30) km/h.
Now, let's use the formula: Time = Distance / Speed
John's family's time to travel 300 km is given by: Time of John = 300 / x
Suzan's family's time to travel 200 km is given by: Time of Suzan = 200 / (x-30)
Since the time taken by both families is the same, we can equate the two equations:
300 / x = 200 / (x-30)
Now, let's solve for x:
Cross-multiply the equation: (300)(x-30) = (200)(x)
300x - 9000 = 200x
300x - 200x = 9000
100x = 9000
Divide both sides by 100: x = 90
Therefore, the speed of John's family vehicle is 90 km/h.
The speed of Suzan's family vehicle is (90-30) = 60 km/h.
To determine the speeds of both vehicles, let's assume that the slower vehicle travels at speed "x" km/h.
According to the given information, the faster vehicle travels at a speed 30 km/h faster than the slower vehicle. So, the speed of the faster vehicle can be represented as "x + 30" km/h.
Now, let's use the formula:
speed = distance/time
For John's family:
Speed of John's family = distance traveled/time taken
= 300 km / t hours (let's assume the time taken is t)
For Suzan's family:
Speed of Suzan's family = distance traveled/time taken
= 200 km / t hours
Since both families take the same amount of time to travel, we can set up the equation:
300/t = 200/t
Cross-multiplying, we get:
300t = 200t
Subtracting 200t from both sides:
100t = 0
Since the equation has no solution, it means that the time taken (t) is zero. This doesn't make sense in the context of the problem, so we can conclude that our assumption (x = t) is incorrect.
To solve this problem, we need additional information. It seems that we cannot determine the speeds of both vehicles without it.