Leah biked down a 12-km mountain road four times as fast as she peddled up the road. If Leah made the round trip up and down the road in 1 hour and 15 minutes, what was her average speed riding downhill?
rate uphill ---- x km/h
rate downhill ---- 4x km/h
12/x + 12/(4x) = 5/4
multiply each term by 4x
48 + 12 = 5x
continue ....
no wonder she rode faster going down, since she didn't have to stop to peddle her wares on the way...
I got x=12. So 12 times 4 equals 48. So she was going 48 km/h downhill. I have a question where did you get the 5/4 from
umhh,
1 hour and 15 minutes
= 1 hour + 1/4 hour
= 5/4 hours
To find Leah's average speed riding downhill, we can use the formula:
Average Speed = Total Distance / Total Time
First, let's find the total distance Leah traveled. Since she biked down the 12-km mountain road four times faster than she pedaled up, we can consider the distance she biked up as 'x' km. Therefore, the distance she biked down would be 12 km.
So, the total distance traveled by Leah is x km (uphill) + 12 km (downhill).
Next, we need to convert the given duration of 1 hour and 15 minutes into hours. There are 60 minutes in an hour, so 15 minutes is equivalent to 15/60 = 0.25 hours.
Now, let's find Leah's total time:
Total Time = Time Uphill + Time Downhill
Since the time it takes Leah to bike downhill is four times faster than going uphill, the time she spent going downhill is 1/4 of the total time.
Therefore, Time Downhill = (1/4) * Total Time = (1/4) * 1.25 hours.
The time it took Leah to bike uphill is (Total Time - Time Downhill) = 1.25 - (1/4) * 1.25 hours.
Now, let's substitute the values into the formula to find the average speed:
Average Speed = Total Distance / Total Time
Average Speed = (x km + 12 km) / 1.25 hours
Remember that the average speed is the speed of biking downhill.