Ms. Driva Reck drove from her home to a service station at 48km/h. She returned home by bicycle at 16km/h. The entire trip took 4 hours. How far was the service station from Ms. Reck's home?
time on bike --- t hours
time driving ---- 4-t hours
16t = 48(4-t)
16t = 192 - 48t
64t = 192
t = 3
so distance = 3(16) = 48 km
To solve this problem, we can use the formula of distance equals speed multiplied by time.
Let's assume the distance from Ms. Reck's home to the service station is "d" kilometers.
When Ms. Reck drove from her home to the service station at 48 km/h, the time taken can be calculated as:
Time1 = Distance/Speed1
Time1 = d/48
When Ms. Reck returned home by bicycle at 16 km/h, the time taken can be calculated as:
Time2 = Distance/Speed2
Time2 = d/16
According to the problem statement, the entire trip took 4 hours. Therefore, we can write the equation:
Time1 + Time2 = 4
Substituting the time values, we get:
d/48 + d/16 = 4
Combining the fractions, we have:
(3d + d)/48 = 4
Simplifying the equation, we get:
4d/48 = 4
Multiply both sides of the equation by 48 to isolate the variable, we get:
4d = 4 * 48
Simplifying further, we get:
4d = 192
Dividing both sides of the equation by 4, we find:
d = 48
Therefore, the service station is 48 kilometers away from Ms. Reck's home.
To find the distance, we can use the formula:
distance = speed × time.
Let's denote the distance from Ms. Reck's home to the service station as "d" km.
When she drove from her home to the service station at 48 km/h, the time taken can be calculated using the formula:
time = distance / speed.
So, the time taken for the first part of the trip is:
t1 = d / 48.
When she returned home by bicycle at 16 km/h, the time taken for the second part of the trip is:
t2 = d / 16.
According to the problem, the entire trip took 4 hours, so we can write this as an equation:
t1 + t2 = 4.
Substituting the values of t1 and t2 in terms of d, we get:
d / 48 + d / 16 = 4.
To solve this equation, we can simplify it by finding a common denominator, which is 48:
(3d + 6d) / 48 = 4.
9d / 48 = 4.
We can now cross-multiply to solve for d:
9d = 192.
Dividing both sides by 9, we find:
d = 192 / 9.
So, the service station is approximately 21.33 km from Ms. Reck's home.