Steve mcspoke left home on his bike traveling at 18km/hr. Steve's brother set out 2 hours later , following the same route, TRAVELING 54 per hour. How long did brother have to travel to catch up with Steve?
Represent the unknown with variable.
Let x = time that Steve's brother travelled
Recall that distance is equal to speed multiplied by time. We get their distances travelled and equate them (since it's said that they followed the same route and they'll overtake at some time):
18(x + 2) = 54x
Note the Steve left two hours before his brother, thus there's +2 on his time. Solving for x,
18x + 36 = 54x
18x - 54x = -36
-36x = -36
x = 1 hour
Hope this helps~ :3
To find the time it takes for Steve's brother to catch up with him, we need to determine when their distances will be equal.
Let's assume the time it takes for Steve's brother to catch up with him is denoted as T (in hours).
In the time T, Steve will have been biking for T + 2 hours, as he left 2 hours earlier.
We can now find the distance traveled by Steve and his brother.
Distance traveled by Steve = Speed of Steve x Time traveled by Steve
Distance traveled by Steve = 18 km/hr x (T + 2) hr
Distance traveled by Steve = 18T + 36 km
Distance traveled by Steve's brother = Speed of brother x Time traveled by brother
Distance traveled by Steve's brother = 54 km/hr x T hr
Distance traveled by Steve's brother = 54T km
Since they meet at the same distance, we can set up an equation:
18T + 36 = 54T
Now let's solve for T:
36 = 54T - 18T
36 = 36T
T = 1
Therefore, it takes Steve's brother 1 hour to catch up with Steve.