Uniform motion Related Problem
Five boy scouts biked to Caliraya lake at 5 km/h. their scout master gave them a ride back home in his pickup car, at 20 kph. Find the hiking time if it 6 hors longer than their riding time.
hiking vs biking, is there a typo ?
let the distance be d
hiking time = d/5
car time = d/20
d/5 - d/20 = 6
times 20
4d - d = 120
3d = 120
d = 40
hiking time = 40/5 = 8 hrs
check:
hiking time = 40/5 = 8
car time = 40/20 = 2
which is a difference of 6 hours, answer is correct
To solve this problem, we can use the formula:
Time = Distance / Speed
Let's assume that the distance between the scouts' home and Caliraya lake is D kilometers.
First, let's calculate the time it took for the scouts to bike to the lake. The speed at which they were biking is 5 km/h, so the time taken is given by:
Time1 = D / 5
Next, let's calculate the time it took for the scout master to drive them back home. The speed at which they were driving is 20 km/h, so the time taken is given by:
Time2 = D / 20
According to the problem statement, the hiking time is 6 hours longer than their riding time. So, we have:
Time1 = Time2 + 6
Now, let's substitute the values of Time1 and Time2 in terms of D into the equation:
D / 5 = D / 20 + 6
To solve this equation, let's multiply both sides by 20 to eliminate the fractions:
4D = D + 120
Now, subtract D from both sides of the equation:
3D = 120
Finally, divide both sides of the equation by 3:
D = 40
So, the distance between the scouts' home and Caliraya lake is 40 kilometers.
To find the hiking time, substitute the value of D into Time1:
Time1 = 40 / 5 = 8 hours
Therefore, the hiking time is 8 hours.