ms. driva reck drove from her home to a service station at 48 km/h. she returned home by bike at 16 km/h. the entire trip took 4 hours. How far was the service station from ms. reck's home?
let the distance be x km
time driving = x/48
time biking = x/16
x/48 + x/16 = 4
times 48
x + 3x = 192
x = 48
Distance was 48 km
check: 48/48 + 48/16 = 1+3 = 4
To find the distance between Ms. Driva's home and the service station, we need to use the formula:
Distance = Speed * Time
Let's calculate the time it took for Ms. Driva to drive to the service station and return home by bike.
Let the distance between her home and the service station be 'd' kilometers.
Time taken to drive to the service station = d/48 (since her speed is 48 km/h)
Time taken to return home by bike = d/16 (since her speed is 16 km/h)
Since the total trip time is 4 hours, the sum of these two times should be equal to 4:
d/48 + d/16 = 4
Now, let's solve this equation to find the value of 'd':
Multiplying the entire equation by the least common multiple (LCM) of 48 and 16, which is 48, we get:
d + 3d = 192
4d = 192
Dividing both sides of the equation by 4:
d = 48
Therefore, the service station is 48 kilometers away from Ms. Driva's home.