Question

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.

Answer 1

Given :-

• 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.

To Find :-

• Find the lengths of the two parts of the journey. ?

Solution :-

Let us assume that, Length of first part is x cm and length of second part is y cm.

Case 1) :- the tortoise walks the first part and crawls the second, it takes 110 seconds.

So,

→ (First Part Distance / walking speed) + (Second part distance / crawling speed) = 110 seconds.

→ (x/4) + (y/3) = 110

→ (3x + 4y) / 12 = 110

→ 3x + 4y = 110 * 12

→ 3x + 4y = 1320 ---------------- Eqn.(1)

Case 2) :- the tortoise crawls the first part and walks the second, it takes 100 seconds.

So,

→ (First Part Distance / crawling speed) + (Second part distance / walking speed) = 110 seconds.

→ (x/3) + (y/4) = 100

→ (4x + 3y) / 12 = 100

→ 4x + 3y = 100 * 12

→ 4x + 3y = 1200 ---------------- Eqn.(2)

Multiply Eqn.(1) by 4 and Eqn.(2) by 3 , and subtracting Eqn.(2) from Eqn.(1) after that, we get,

→ 4(3x + 4y) - 3(4x + 3y) = 4*1320 - 3*1200

→ 12x - 12x + 16y - 9y = 5280 - 3600

→ 7y = 1680

dividing both sides by 7,

→ y = 240 cm. (Ans.)

Putting value of y in Eqn.(1) Now,

→ 3x + 4*240 = 1320

→ 3x = 1320 - 960

→ 3x = 360

dividing both sides by 3,

→ x = 120 cm. (Ans.)

Hence, First part is 120cm long and second part is 240cm long.

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Answer 2

Step-by-step explanation:

Given 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.

• Given tortoise makes a journey in two parts.
• Let the lengths of the journey be m and n
• So speed of tortoise if it walks will be 4 cm/s
• Speed of the tortoise if it crawls will be 3 cm/s
• According to the question we have
•                                     Distance = speed x time
•                                      Or time = distance / speed
• So m/4 + n/3 = 110
•      3m + 4n / 12 = 110
•      3m + 4n = 1320 --------------1
• Now for the second part we have the equation
• So m/3 + n/4 = 100
•        4m + 3n / 12 = 100
•        4m + 3n = 1200 ---------------2
•    3m + 4n = 1320 x 4
•    4m + 3n = 1200 x 3
•      
•   12m + 16 n = 5280
•  12m + 9n = 3600
•              7n = 1680
•          Or n = 240 cm  
• 3m + 4(240) = 1320
• 3m + 960 = 1320
• 3m = 360
• Or m = 120 cm
• The length of first part of journey is 120 cm and that of second part will be 240 cm

Reference link will be

https://brainly.in/question/9124088