Difference between revisions of "1997 PMWC Problems/Problem T4"
m (→See also) |
Vanstraelen (talk | contribs) |
||
| Line 4: | Line 4: | ||
==Solution== | ==Solution== | ||
{{solution}} | {{solution}} | ||
| + | |||
| + | Time <math>t</math>, velocity <math>v</math>, distance <math>a</math>, formula <math>v=\frac{a}{t}</math> or <math>a=v \cdot t</math>. | ||
| + | Time of departure <math>T</math>. | ||
| + | First, ferry 1: <math>a_{1}=v_{1}(8.20-T)</math> and ferry 2: <math>a_{2}=v_{2}(8.20-T)</math>; sum <math>a=a_{1}+a_{2}=(v_{1}+v_{2})(8.20-T)</math>. | ||
| + | Second, difference in time: <math> 9.11-8.20-0.15=0.36</math>. | ||
| + | Ferry 1: <math>a_{2}+a_{4}=v_{1}\cdot (0.36)</math> and ferry 2: <math>a_{1}+a_{3}=v_{2}\cdot (0.36)</math>; sum <math>2a=(v_{1}+v_{2})(0.36)</math>. | ||
| + | Dividing: <math>\frac{1}{2}=\frac{8.20-T}{0.36}</math>, so <math>T=8.02</math>. | ||
==See Also== | ==See Also== | ||
Revision as of 14:25, 3 June 2013
Problem
In one morning, a ferry traveled from Hong Kong to Kowloon and another ferry traveled from Kowloon to Hong Kong at a different speed. They started at the same time and met first time at 8:20. The two ferries then sailed to their destinations, stopped for 15 minutes and returned. The two ferries met again at 9:11. Suppose the two ferries traveled at a uniform speed throughout the whole journey, what time did the two ferries start their journey?
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
Time 
, velocity 
, distance 
, formula 
or 
.
Time of departure 
.
First, ferry 1: 
and ferry 2: 
; sum 
.
Second, difference in time: 
.
Ferry 1: 
and ferry 2: 
; sum 
.
Dividing: 
, so 
.
See Also
| 1997 PMWC (Problems) | ||
| Preceded by Problem T3 |
Followed by Problem T5 | |
| I: 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 T: 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
