Rate Problems Revisited

[SCSmith]

Daphne and Niles are both driving west on Route 66. At 4:00, Daphne is 5 miles west of Niles. A little later, Niles passes Daphne. If Niles is driving at 55 miles per hour and Daphne at 50 miles per hour, at what time does Niles pass Daphne?
RxT=D so;
Daphne's rate: 50 x Daphne's Time which is 5 more miles than Niles: t+5 = D: which is 50(t+5).
Niles rate and time: 55 x t =D which is 55t. The distances are equivalent so I believe the equation should be: 50(t+5)=55t
50t + 250 = 55t
5t = 250
t = 50
The problem I have is the units don't match, converting miles to hours. Is the answer suppose to be 50minutes/60minutes or .50hours which would be 30 minutes. Either way 50/60 comes out to be 48 additional minutes giving me an answer of 4:48 being the time Niles passes Daphne or the other answer being 4:30. Both these answers are wrong, the right answer is 5:00

 

[Denis]

Daphne and Niles are both driving west on Route 66. At 4:00, Daphne is 5 miles west of Niles. A little later, Niles passes Daphne. If Niles is driving at 55 miles per hour and Daphne at 50 miles per hour, at what time does Niles pass Daphne?
RxT=D so;
Daphne's rate: 50 x Daphne's Time which is 5 more miles than Niles: t+5 = D: which is 50(t+5).
Niles rate and time: 55 x t =D which is 55t. The distances are equivalent so I believe the equation should be: 50(t+5)=55t
50t + 250 = 55t
5t = 250
t = 50
The problem I have is the units don't match, converting miles to hours. Is the answer suppose to be 50minutes/60minutes or .50hours which would be 30 minutes. Either way 50/60 comes out to be 48 additional minutes giving me an answer of 4:48 being the time Niles passes Daphne or the other answer being 4:30. Both these answers are wrong, the right answer is 5:00

C'mon Smitty; keep it SIMPLE:
formula is simple: speed = distance divided by time : quit jerking it all over

Daphne travels m miles after 4pm before Niles catches up;
so Niles travels m + 5 miles.

The time is the same for both: h hours.

Daphne: 50 = m / h : m = 50h
Niles: 55 = (m + 5) / h : m = 55h - 5

SO: 50h = 55h - 5 : finish it!