Answer:
1:30 pm
Explanation:
You want the time when Sahil catches up to Joaquin, who left at 8 am riding 50 mph when Sahil left at 8:30 am, riding at 55 mph.
Time, Speed, Distance
The relation between time, speed, and distance is ...
distance = speed × time
time = distance / speed
Joaquin has a head start of 0.5 hours (30 minutes), during which time he traveled ...
head start distance = (50 mi/h) × (0.5 h) = 25 mi
Sahil is traveling 55 - 50 = 5 mph faster than Joaquin, so closes that gap at the rate of 5 mi/h. The time it takes to close the gap entirely is ...
time = distance / speed = 25 mi / (5 mi/h) = 5 h
So, 5 hours after Sahil starts at 8:30, the two riders will be at the same place.
Sahil catches Joaquin at 1:30 pm.
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Additional comment
By the time the gap is closed at 1:30 pm, both riders will have traveled a distance of ...
distance = speed × time = 50 mi/h × 5.5 h = 55 mi/h × 5 h = 275 mi
In the attached graph, we have written equations for the total distance traveled by each motorcycle. The x-value used is the clock time on a 24-hour clock. That is, their meeting time of 13.5 hours corresponds to 13:30 hours or 1:30 p.m. on a 12-hour clock.