A man cycles to a village at 18km/h and returns at 12km/h. If it takes 6 1|2 hours for the double journey, how far does he ride all together
I think 93.6km is not the answer. It should be 90km
The distance each way would of course be the same.
let that distance be x km
x/18 + x/12 = 6.5
I would now multiply each term by 36, the LCM to have nice whole numbers
then solve for x
Let me know what you get.
To find the total distance the man rides, we need to determine the distances traveled in each direction separately.
Let's call the distance to the village 'd' (in kilometers).
The time it takes to cycle to the village is given by the formula: time = distance / speed.
So, the time taken to cycle to the village is: t1 = d / 18.
Similarly, the time taken to return from the village is: t2 = d / 12.
The total time for the round trip is given as 6 1/2 hours. We can express this as: t1 + t2 = 6.5.
Substituting the expressions for t1 and t2: (d / 18) + (d / 12) = 6.5.
To solve this equation, we can multiply it by the least common multiple (LCM) of 18 and 12, which is 36.
36 * [(d / 18) + (d / 12)] = 36 * 6.5.
Simplifying, we get: 2d + 3d = 234.
Combining like terms: 5d = 234.
Dividing both sides by 5, we find: d = 234 / 5.
Therefore, the distance to the village is d = 46.8 km.
Since the man travels this distance twice (to and from the village), the total distance he rides is 46.8 km + 46.8 km = 93.6 km.
So, he rides a total of 93.6 kilometers all together.
d1 = d2.
18*T = 12*(6.5-T).
Divide both sides by 6:
3T = 2(6.5 - T),
3T = 13 - 2T,
T = 2.6 h. to the village.
d1 = 18*T = 18*2.6 = 46.8 km to the village. =
d1 + d2 = 46.8 + 46.8 = 93.6 km.