Hello, nick29!
Aloha is correct . . .
Alexis left Miami and drove at a speed of 20 kph.
Tom Left 3 hours later and drove at a speed of 30 kph.
How long will it take Tom to catch up to Alexis?
Let T = number of hours for Tom to catch up to Alexis.
Alexis had a 3-hour headstart; she drove 60 km already.
At that instant, Tom starts at 30 kph.
And they both drive for T hours.
Alexis has gone:
.60 + 20T km
. Tom has gone:
.30T km
Since their distances are equal:
.30T
.=
.20T + 60 . . . and solve for T.
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This problem lends itself to an "eyeball" solution.
Alexis is 60 km ahead of Tom.
The difference of their speeds is:
.30 - 20 = 10 kph
. . It is
as if Alexis is parked and Tom is driving toward her at 10 kph.
At 10 kph, how long will it take Tom to drive 60 km? . . . 6 hours!
