Road trip here we go
Daniel drives at a speed of 90 and Kent drives at a speed of 60. They both started from A and B respectively at the same time on the opposite side facing each other.
After reaching C which is a place at somewhere between A and B, Kent reached earlier than Daniel by 10 minute; The second day, after reaching thier destination, Daniel and Kent started from B amd A respetively to drive back to their original starting point.
This time, Daniel was earlier than Kent by 1.5 hours after reaching C. Find the distance from A to B.
The answer is 240.
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1 solution
Remember that point C always stays at the same place.
On the first day, Daniel and Kent travelled x hours before one reached point C. Daniel travelled at a speed of 1.5 miles per minute, while Kent travelled at a speed of 1 mile per minute. When Kent reached point C, Daniel was 15 miles away from point C. Therefore, the distance from point B (where Kent began) to point C is 60x miles, and the distance from point A (where Daniel began) to point C is 90x+15 miles.
On the second day, Daniel and Kent travelled y hours before one reached point C. Daniel reached point C first, so the distance from point B to point c is 90y miles. Kent travelled 60y miles already, and still had 90 miles left, so the distance from point A to point C is 60y+90 miles.
We can now form a system of linear equations. The distance from point A to point C is 90x+15 or 60y+90, and the distance from point B to C is 60x or 90y. With that, we have this system of linear equations: 90x+15=60y+90, and 60x=90y
By solving this system of equations through elimination, substitution, or setting 2 equations equal to each other, we get y=1 and x=1.5.
The distance from point A to B is the distance from point A to C plus the distance from point B to C. We can substitute y as 1 into 60y+90+90y (or x as 1 into 90x+15+60x if you prefer), to get 240.