Mrs .Smith walk 3/8 of a journey and took a taxi for a further half of the journey and walk the remaining 2 kilometers
A)how long was the entire journey?
B)what was the total distance walked?
C)how far did she travel by taxi?
To find the answer to these questions, we need to analyze the given information step by step.
A) The entire journey consists of three parts: the distance walked in the first part, the distance covered by taxi in the second part, and the distance walked in the third part. Let's represent the total distance of the journey as "x" kilometers.
In the first part, Mrs. Smith walks 3/8 of the journey. So, this distance can be calculated by multiplying 3/8 by "x":
Distance walked in the first part = (3/8) * x
In the second part, Mrs. Smith takes a taxi for half of the journey. So, this distance can be calculated by multiplying 1/2 by "x":
Distance covered by taxi = (1/2) * x
In the third part, Mrs. Smith walks the remaining 2 kilometers.
Now, considering the entire journey, we can add up the distances walked in each part to find the total distance:
x = (3/8) * x + (1/2) * x + 2
To solve this equation, we need to simplify it:
x = 3/8 * x + 1/2 * x + 2
x = 6/8 * x + 4/8 * x + 2
x = 10/8 * x + 2
Next, we'll move all the terms involving "x" to one side of the equation:
x - 10/8 * x = 2
2/8 * x = 2
Now, we can isolate "x" by multiplying both sides of the equation by 8/2:
x = 2 * 8/2
x = 16/2
x = 8
Therefore, the entire journey was 8 kilometers long.
B) To find the total distance walked, we need to add up the distances walked in the first and third parts. Using the values we calculated earlier:
Distance walked in the first part = (3/8) * x
Distance walked in the first part = (3/8) * 8
Distance walked in the first part = 3 kilometers
Distance walked in the third part = 2 kilometers
Total distance walked = Distance walked in the first part + Distance walked in the third part
Total distance walked = 3 kilometers + 2 kilometers
Total distance walked = 5 kilometers
Therefore, Mrs. Smith walked a total distance of 5 kilometers.
C) To find the distance traveled by taxi, we need to subtract the total distance walked from the entire journey distance:
Distance covered by taxi = Entire journey distance - Total distance walked
Distance covered by taxi = 8 kilometers - 5 kilometers
Distance covered by taxi = 3 kilometers
Therefore, Mrs. Smith traveled 3 kilometers by taxi.
J is journey length.
J=3/8*J + .5J+2km
1/8 J=2km
J=16km
walked=3/8 J + 2
taxi=1/2 J
2 km + (3/8)j + (1/2)j = 1 j
2km = (8/8 - 4/8 - 3/8)j
2 km = j/8
j = 16 km total
you do the rest now :)
To find the answers, let's break down the information given:
Given:
- Mrs. Smith walked 3/8 of the journey.
- Mrs. Smith took a taxi for a further half of the journey.
- Mrs. Smith walked the remaining 2 kilometers.
A) To find the entire journey's length, we need to find the total distance traveled.
First, let's find the distance walked and taken by taxi individually:
Distance walked:
3/8 of the journey = (3/8) * total distance = 3/8 * D
Distance taken by taxi:
Half of the journey = (1/2) * total distance = 1/2 * D
Next, we add the distance walked and taken by taxi to find the total distance traveled:
Total distance traveled = Distance walked + Distance taken by taxi + Distance walked remaining
Total distance traveled = 3/8 * D + 1/2 * D + 2
Since we know that the remaining distance walked is 2 kilometers, we can set up an equation:
2 = 3/8 * D + 1/2 * D + 2
Simplifying the equation:
2 = (3/8 + 1/2) * D + 2
2 = (6/16 + 8/16) * D + 2
2 = (14/16) * D + 2
2 - 2 = (14/16) * D
0 = (14/16) * D
Since D cannot be zero, this means:
14/16 * D = 0
Therefore, the entire journey's length cannot be determined with the given information.
B) The total distance walked is the sum of the distance Mrs. Smith initially walked and the distance she walked remaining.
Total distance walked = Distance walked + Distance walked remaining
Total distance walked = 3/8 * D + 2
C) The distance traveled by taxi is half of the journey.
Distance traveled by taxi = Distance taken by taxi
Distance traveled by taxi = 1/2 * D
Note: Without knowing the value of D (the total distance of the journey), we cannot provide numerical answers for parts A, B, or C.