Algebra math problem help?
Some bank robbers leave town, speeding at 70mph. ten minutes later, the police give chase, traveling 78mph. How long will it take the police to overtake the robbers?
Can someone show how you set up the problem?
Some bank robbers leave town, speeding at 70mph. ten minutes later, the police give chase, traveling 78mph. How long will it take the police to overtake the robbers?
Can someone show how you set up the problem?
Comments
Use the distance equation d = rt. When the police nab the crooks, they will have traveled equal distances, so we can equate d = rt, where r and t are the speed and travel time of the police, with d' = r't', where r' and t' are the speed and travel time of the robbers. Since the robbers have been traveling 10 minutes = 1/6 hr longer than the police, then we can let t' = t + 1/6 hr.
d(1) = d(2)
rt = r't' = r' (t + 1/6)
78 mph(t hrs) = (70 mph)(t + 1/6 hr) Recall: 10 min = 1/6 hr
78t = 70t + (70/6)
8t = (70/6)
t = (70/6)/8
t = 70/48
t = 35/24
t = 1 and 11/24 hrs.
To check, verify the distances are equal:
rt = r' (t + 1/6)
78 mi/hr∙(35/24) hr = 70 mi/hr∙(35/24 + 4/24) hr
78 (35/24) = 70 (39/24)
2730/24 = 2730/24
113.75 mi = 113.75 mi
The equation balances, so we have the right time:
It will take the cops 1 and 11/24 hours to catch the robbers.
All I can say is that the cops better hope the crooks don't turn off onto a side road, or they will be going on a wild goose chase. They need a rocket propelled patrol car with a lead on them like that.