Question:-
After traveling a distance of 32 [tex]\frac{4}{5}[/tex]km, Amera found that she is still to cover [tex]\frac{5}{7}[/tex] of the whole distance. what is the total distance covered by amera.
•This is very easy question but the answer should come 114[tex]\frac{4}{5}[/tex] km
• Note:-follow app rules dont copy it from any web answer on your on
•Take your time to answer
•Thanks in advance for Answer
Answer:
[tex]\sf Total \ Distance = 114\dfrac{4}{5} \ km[/tex]
Step-by-step explanation:
Given;
[tex]\sf \dashrightarrow \textsf{Distance covered by Amera} = \sf 32\dfrac{4}{5} \ km[/tex]
[tex]\sf \dashrightarrow \textsf{Part of the total distance that needs to be covered} \\\textsf{ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ in order to cover the full distance}[/tex] [tex]= \sf \dfrac{5}{7} \times Whole \ Distance[/tex]
Let the Whole distance be “D”, therefore;
[tex]\sf \dashrightarrow \textsf{Part of the total distance that needs to be covered} \\\textsf{ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ in order to cover the full distance}[/tex] [tex]= \sf \dfrac{5}{7}D[/tex]
We know that;
[tex]\dashrightarrow \textsf{ Distance covered} \ + \textsf{ Part of the total distance} \\\textsf{\ \ \ \ \ \ \ \ \ \ By Amera \ \ \ \ \ \ \ \ \ \ that needs to be covered to} \ \ \sf = Total \ Distance \\\textsf{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ complete the whole distance}[/tex]
On substituting the values we get;
[tex]\sf \dashrightarrow \ 32\dfrac{4}{5} \ + \ \dfrac{5D}{7} \ = \ D[/tex]
[tex]\sf \dashrightarrow \ 32\dfrac{4}{5} \ = \ D \ – \dfrac{5D}{7}[/tex]
On converting the mixed fractions to improper fractions we get;
[tex]\sf \dashrightarrow \ \dfrac{(32 \times 5) + 4}{5} \ = \ D \ – \ \dfrac{5D}{7}[/tex]
[tex]\sf \dashrightarrow \ \dfrac{(160) + 4}{5} \ = \ D \ – \ \dfrac{5D}{7}[/tex]
[tex]\sf \dashrightarrow \ \dfrac{164}{5} \ = \ D \ – \ \dfrac{5D}{7}[/tex]
On taking LCM in the RHS we get;
[tex]\sf \dashrightarrow \ \dfrac{164}{5} \ = \ \dfrac{7D – 5D}{7}[/tex]
[tex]\sf \dashrightarrow \ \dfrac{164}{5} \ = \ \dfrac{2D}{7}[/tex]
On transposing 7 to the LHS we get;
[tex]\sf \dashrightarrow \ \dfrac{164 \times 7}{5} \ = \ \dfrac{2D}{1}[/tex]
[tex]\sf \dashrightarrow \ \dfrac{1148}{5} \ = \ \dfrac{2 \times D}{1}[/tex]
On transposing 2 to the LHS we get;
[tex]\sf \dashrightarrow \ \dfrac{1148}{5 \times 2} \ = \ D[/tex]
On dividing 1148 and 2 we get;
[tex]\sf \dashrightarrow \ \dfrac{574}{5} \ = \ D[/tex]
On converting the improper fraction to a mixed fraction we get; [Refer to the attachment]
[tex]\sf \dashrightarrow D = 114\dfrac{4}{5} \ km.[/tex]
Therefore, the total distance covered by Amera is 114 ⁴/₅ km.
[Please view the answer on the website if the lines look cluttered on the app]
Let Amera has to cover x km distance
Then, she still has to cover 5x/7 distance
she covered (x- 5x/7)-2x/7 distance
So,
=> 2x/7=164/5
=> x= 114.8 kms
so, the total distance is 114.8 kms