The work and solution to:
Stefan is bicycling on a bike trail at an average of 10 miles per hour. Erik starts bicycling on the same trail 30 minutes later at 16 miles per hour. How long will it take Erik to pass Stefan?
Speed of Stefan = 10mph
Speed of Erik = 16mph
Stefan has a 30 min head start.
30 min = 0.5 hours
We know that:
16t = 5 + 10t
6t = 5
t = 5/6 hours
t = 50 minutes.
Erik will pass Stefan in 50 minutes after Erik starts the trail.
Hope this helps :)
Yes, that's correct! Good job!
10(t + 1/2)=16t .
Expand the bracket. 10t + 10/2 =16t. Collect like terms
10/2 =16t - 10t.
10/2 = 6t.
5 = 6t
T =5/6.
no
the answer is supposed to be 50 min
idk how to do it but that's the answer written in my textbook
To solve this problem, we need to determine at what point Erik catches up to Stefan.
Let's break down the problem:
Stefan is already on the bike trail, moving at a constant speed of 10 miles per hour.
Erik starts 30 minutes later and is moving at a faster speed of 16 miles per hour.
Since Erik is cycling faster than Stefan, he will eventually catch up to him.
First, let's convert the 30 minutes delay that Erik starts into hours.
30 minutes is equal to 30/60 = 0.5 hours.
Now, let's calculate the distance Stefan covers in the 0.5-hour head start.
Distance = Speed * Time
Distance = 10 miles/hour * 0.5 hours
Distance = 5 miles
Stefan has a 5-mile lead over Erik.
Now, let's find out how long it will take Erik to cover this 5-mile gap.
Since both Stefan and Erik are moving on the same bike trail, their distances covered will be the same when Erik catches up.
Let's assume it takes Erik "t" hours to catch up to Stefan.
Distance covered by Stefan = Distance covered by Erik
Now, let's write an equation using their speeds and times:
10 miles/hour * t = 16 miles/hour * (t - 0.5)
We subtract 0.5 from Erik's time (t - 0.5) because Stefan had a 0.5-hour head start.
Let's solve this equation:
10t = 16(t - 0.5)
10t = 16t - 8
8 = 6t
t = 8/6
t = 4/3
So, it will take Erik 4/3 hours to catch up to Stefan.
Let's convert this time into minutes:
4/3 hours * 60 minutes/hour = 80 minutes
Therefore, it will take Erik 80 minutes to pass Stefan.
at time t hours after Erik started, we need to have the distances equal. Since Stefan started 1/2 hour earlier than Erik,
10(t + 1/2) = 16t
solve for t, and that is how many hours Erik had to ride.