Susan begins counting backward from $1298$ by $4' s$ , saying one number every $5 seconds$ . At the same time, Jim begins counting forward from $171$ by $3' s$ , saying one number every $5 seconds$ . What number will they both say at the same time?

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Solution

Step-1: Find the time at which both say the same number:
Given that,
Susan begins counting backward from $1298$ by $4' s$ , saying one number every $5 seconds$
Jim begins counting forward from $171$ by $3' s$ , saying one number every $5 seconds$
As both Susan and Jim starts at the same time, so let both of them say the same number after time $t seconds$ .
Thus, after $t seconds$ , Susan will say a number $1298 - 4 t$ $. . . (i)$
And after $t seconds$ , Jim will say a number $171 + 3 t$ $. . . (ii)$
So, $1298 - 4 t = 171 + 3 t$
$\Rightarrow$ $1298 - 171 = 4 t + 3 t$
$\Rightarrow$ $1127 = 7 t$
$\Rightarrow$ $161 = t$
Step-2: Find the required number:
Now, substitute $t = 161 seconds$ in any one of the equation $(i)$
So, $1298 - 4 t = 1298 - 4 (161)$
$\Rightarrow$ $= 1298 - 644$
$\Rightarrow$ $= 654$
Hence, the required number is $654$ .

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Susan begins counting backward from 1298by 4's, saying one number every 5seconds. At the same time, Jim begins counting forward from 171by 3's, saying one number every 5seconds. What number will they both say at the same time?

Susan begins counting backward from $1298$ by $4' s$ , saying one number every $5 seconds$ . At the same time, Jim begins counting forward from $171$ by $3' s$ , saying one number every $5 seconds$ . What number will they both say at the same time?