SOLUTION: A tortoise makes a journey in two parts; it can either walk at 4 cm/s or crawl at 3 cm/s. If the tortoise walks the first part and crawls the second, it takes 110 seconds. If it cr

Question 1195601: A tortoise makes a journey in two parts; it can either walk at 4 cm/s or crawl at 3 cm/s. If the tortoise walks the first part and crawls the second, it takes 110 seconds. If it crawls the first part and walks the second, it takes 100 seconds. Find the lengths of the two parts of the journey.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52814) (Show Source): You can put this solution on YOUR website!
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A tortoise makes a journey in two parts; it can either walk at 4 cm/s or crawl at 3 cm/s.
If the tortoise walks the first part and crawls the second, it takes 110 seconds.
If it crawls the first part and walks the second, it takes 100 seconds.
Find the lengths of the two parts of the journey.
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Let x be the length of the 1st part of the journey, and let y be the length of the 2nd part of the journey. In the first scenario, the travel time is + . In the second scenario, the travel time is + . Therefore, from the problem's description we have this system of two equations in two unknowns + = 110 seconds (1) + = 100 seconds (2) To simplify it, multiply equations (1) and (2) by 12 (both sides). You will get then 4x + 3y = 1320 (3) 3x + 4y = 1200 (4) Solve it using the Elimination method. Multiply equation (3) by 3; multiply equation (4) by 4. You will get 12x + 9y = 3960 (5) 12x + 16y = 4800 (6) Subtract eq(5) from eq(6). You will get 16y - 9y = 4800 - 3960 7y = 840 y = 840/7 = 120. Next find x, substituting y= 120 into equation (3). 4x + 3*120 = 1320 --> 4x = 1320 - 3*120 --> 4x = 960 --> x = 960/4 = 240. ANSWER. First part of the journey is 240 cm. Second part of the journey is 120 cm. CHECK. Make checking on your own by substituting the found values of x and y into equations (1) and (2).

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Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

The response from the other tutor shows a good standard method for solving the problem.

But the numbers in this problem allow for a somewhat different solution method that some students might (or might not!) find easier.

If x and y are the lengths of the first and second parts of the journey respectively, then we have two equations:

Multiply both equations by the least common denominator, 3*4=12:

[1]
[2]

Now, instead of using the standard algebraic method of solving the pair of equation using elimination, let's add these last two equations and simplify:

Now use this equation with equations [1] and [2] to solve the problem.

[3]
[1]

Subtract [3] from [1]:

[3]
[2]

Subtract [3] from [2]:

Obviously we get the same answers -- by a different path.

ANSWERS: The first part of the journey is x=120cm; the second part is y=240cm.

CHECK:
x/4+y/3 = 120/4+240/3 = 30+80 = 110
x/3+y/4 = 120/3+240/4 = 40+60 = 100

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