Sunday, March 9, 2008

Time and Distance Problem 2 Solution

 Here's the answer to the time and distance problem # 2 that read, "Bob leaves in his car driving at a constant speed of 40 miles/hour. 4 hours later Steve leaves going the same direction at 60 miles/hour. How long will it take until Steve catches up (is side by side) with Bob?"

A non algebra solution would be to realize that Steve is moving 20 miles/hour faster than Bob and has to cover 160 miles (40 * 4) to catch up to Bob (40 miles/hour X 4 hours = 160 miles) So how long until does it take to cover 160 miles going 20 miles/hour-- 8 hours

Algebraically you got 40(x+4) = 60x where x is time and x + 2 means 2 hours ahead

So, 40x + 160 = 60x which makes

160 = 20x ... x = 160/20 = 8 ----

So in 8 hours they meet.


  1. is this the right answer? the problem says
    bob leaves in 40mph, then 4 hours later steve follows at 60mph, so it must be:

    coz bob has 4 hrs more than steve so x+4
    160/20 = 8 hrs

    ok now lets check it.

    it says bob drives for 40mph and steve drives 60miles per hour. So if steve drives for 8 hours he will be in (d=s*t)60mph*8hrs = 480miles
    and bob drives for 40mph noting that steve follows AFTER 4hrs so in 8 hrs that steve drives
    its equal to 12hrs or 8hrs(steve)+4hrs(bob) so it will be 40mph*12hrs=480.
    it make sense they meet up at 480miles away in 8hrs.

    check about the answer above it says 4hrs, so if steve drives for 4hrs; 60*4=240miles
    and bob drives for 8hrs; 40*8=320miles
    they did not catch up coz bob is at 320 miles away and steve is just at 240 miles away.

  2. anonymous -- u are correct -- it was a case of bad arithmetic -- i meant 160 not 80 miles since 40 * 4 is 160 == I was solving for 80 so its half of the correct answer - it should be 8 hours...

  3. or actually i made the mistake of time - i was answering for 2 hours not 4 -


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